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JuliaFEM.jl/notebooks/2015-12-18-normal-tangential-coordinates.ipynb
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Jukka Aho 5426e47a26 more general way to define saddle point problem.
2015-12-23 01:52:28 +02:00

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Normal-tangential coordinates\n",
"\n",
"Author: Jukka Aho\n",
"\n",
"**Abstract**: Use of normal tangential coordinate system"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"Array{Float64,1}"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using JuliaFEM.Core: Quad4, Seg2, Seg3, PlaneStressLinearElasticityProblem, DirichletProblem, update!, DirectSolver\n",
"typealias Node Vector{Float64}"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"using Gadfly\n",
"set_default_plot_size(10cm, 10cm)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Element normal definition in 2d"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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" return factory(Snap);\n",
" });\n",
" } else {\n",
" // Browser globals (glob is window)\n",
" // Snap adds itself to window\n",
" glob.Gadfly = factory(glob.Snap);\n",
" }\n",
"}(this, function (Snap) {\n",
"\n",
"var Gadfly = {};\n",
"\n",
"// Get an x/y coordinate value in pixels\n",
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"\n",
"var yPX = function(fig, y) {\n",
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"};\n",
"\n",
"\n",
"Snap.plugin(function (Snap, Element, Paper, global) {\n",
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" }\n",
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" }\n",
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" };\n",
"\n",
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" return {\n",
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" x1: bbox.x + bbox.width,\n",
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" y1: bbox.y + bbox.height\n",
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" };\n",
"\n",
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" var root = this.plotroot()\n",
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" return {\n",
" x: bbox.x + bbox.width / 2,\n",
" y: bbox.y + bbox.height / 2\n",
" };\n",
" };\n",
"\n",
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"\n",
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" if (event.type != \"mouseover\" && event.type != \"mouseout\") {\n",
" return;\n",
" }\n",
"\n",
" var reltg = event.relatedTarget ? event.relatedTarget :\n",
" event.type == \"mouseout\" ? event.toElement : event.fromElement;\n",
" while (reltg && reltg != this.node) reltg = reltg.parentNode;\n",
"\n",
" if (reltg != this.node) {\n",
" return fn.apply(this, event);\n",
" }\n",
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"\n",
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"\n",
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" fn2);\n",
"\n",
" return this;\n",
" };\n",
"\n",
"\n",
" // Snap's attr function can be too slow for things like panning/zooming.\n",
" // This is a function to directly update element attributes without going\n",
" // through eve.\n",
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" } else {\n",
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" return this;\n",
" }\n",
" };\n",
"\n",
" Element.prototype.init_gadfly = function() {\n",
" this.mouseenter(Gadfly.plot_mouseover)\n",
" .mouseleave(Gadfly.plot_mouseout)\n",
" .dblclick(Gadfly.plot_dblclick)\n",
" .mousewheel(Gadfly.guide_background_scroll)\n",
" .drag(Gadfly.guide_background_drag_onmove,\n",
" Gadfly.guide_background_drag_onstart,\n",
" Gadfly.guide_background_drag_onend);\n",
" this.mouseenter(function (event) {\n",
" init_pan_zoom(this.plotroot());\n",
" });\n",
" return this;\n",
" };\n",
"});\n",
"\n",
"\n",
"// When the plot is moused over, emphasize the grid lines.\n",
"Gadfly.plot_mouseover = function(event) {\n",
" var root = this.plotroot();\n",
"\n",
" var keyboard_zoom = function(event) {\n",
" if (event.which == 187) { // plus\n",
" increase_zoom_by_position(root, 0.1, true);\n",
" } else if (event.which == 189) { // minus\n",
" increase_zoom_by_position(root, -0.1, true);\n",
" }\n",
" };\n",
" root.data(\"keyboard_zoom\", keyboard_zoom);\n",
" window.addEventListener(\"keyup\", keyboard_zoom);\n",
"\n",
" var xgridlines = root.select(\".xgridlines\"),\n",
" ygridlines = root.select(\".ygridlines\");\n",
"\n",
" xgridlines.data(\"unfocused_strokedash\",\n",
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"\n",
" // emphasize grid lines\n",
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"\n",
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"\n",
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"};\n",
"\n",
"// Reset pan and zoom on double click\n",
"Gadfly.plot_dblclick = function(event) {\n",
" set_plot_pan_zoom(this.plotroot(), 0.0, 0.0, 1.0);\n",
"};\n",
"\n",
"// Unemphasize grid lines on mouse out.\n",
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"\n",
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"\n",
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"\n",
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" .selectAll(\"path\")\n",
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"\n",
" destcolor = root.data(\"unfocused_ygrid_color\");\n",
" ygridlines.attribute(\"stroke-dasharray\", ygridlines.data(\"unfocused_strokedash\"))\n",
" .selectAll(\"path\")\n",
" .animate({stroke: destcolor}, 250);\n",
"\n",
" // hide zoom slider\n",
" root.select(\".zoomslider\")\n",
" .animate({opacity: 0.0}, 250);\n",
"};\n",
"\n",
"\n",
"var set_geometry_transform = function(root, tx, ty, scale) {\n",
" var xscalable = root.hasClass(\"xscalable\"),\n",
" yscalable = root.hasClass(\"yscalable\");\n",
"\n",
" var old_scale = root.data(\"scale\");\n",
"\n",
" var xscale = xscalable ? scale : 1.0,\n",
" yscale = yscalable ? scale : 1.0;\n",
"\n",
" tx = xscalable ? tx : 0.0;\n",
" ty = yscalable ? ty : 0.0;\n",
"\n",
" var t = new Snap.Matrix().translate(tx, ty).scale(xscale, yscale);\n",
"\n",
" root.selectAll(\".geometry, image\")\n",
" .forEach(function (element, i) {\n",
" element.transform(t);\n",
" });\n",
"\n",
" bounds = root.plotbounds();\n",
"\n",
" if (yscalable) {\n",
" var xfixed_t = new Snap.Matrix().translate(0, ty).scale(1.0, yscale);\n",
" root.selectAll(\".xfixed\")\n",
" .forEach(function (element, i) {\n",
" element.transform(xfixed_t);\n",
" });\n",
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" var cx = element.asPX(\"x\"),\n",
" cy = element.asPX(\"y\");\n",
" var st = element.data(\"static_transform\");\n",
" unscale_t = new Snap.Matrix();\n",
" unscale_t.scale(1, 1/scale, cx, cy).add(st);\n",
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"\n",
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" element.attr(\"visibility\",\n",
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" }\n",
"\n",
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" var yfixed_t = new Snap.Matrix().translate(tx, 0).scale(xscale, 1.0);\n",
" var xtrans = new Snap.Matrix().translate(tx, 0);\n",
" root.selectAll(\".yfixed\")\n",
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" element.transform(yfixed_t);\n",
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" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
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" cy = element.asPX(\"y\");\n",
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"\n",
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" }\n",
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"\n",
" // we must unscale anything that is scale invariance: widths, raiduses, etc.\n",
" var size_attribs = [\"font-size\"];\n",
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" }\n",
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" .forEach(function (element, i) {\n",
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" cy = element.attribute(\"cy\");\n",
" unscale_t = new Snap.Matrix().scale(1/xscale, 1/yscale,\n",
" cx, cy);\n",
" element.transform(unscale_t);\n",
" return;\n",
" }\n",
"\n",
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" element.attribute(key, val * old_scale / scale);\n",
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"\n",
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"// Find the most appropriate tick scale and update label visibility.\n",
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" if (!root.hasClass(axis + \"scalable\")) return;\n",
"\n",
" var tickscales = root.data(axis + \"tickscales\");\n",
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" var best_tickscale_dist = Infinity;\n",
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" };\n",
"\n",
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" };\n",
"\n",
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" }\n",
"};\n",
"\n",
"\n",
"var set_plot_pan_zoom = function(root, tx, ty, scale) {\n",
" var old_scale = root.data(\"scale\");\n",
" var bounds = root.plotbounds();\n",
"\n",
" var width = bounds.x1 - bounds.x0,\n",
" height = bounds.y1 - bounds.y0;\n",
"\n",
" // compute the viewport derived from tx, ty, and scale\n",
" var x_min = -width * scale - (scale * width - width),\n",
" x_max = width * scale,\n",
" y_min = -height * scale - (scale * height - height),\n",
" y_max = height * scale;\n",
"\n",
" var x0 = bounds.x0 - scale * bounds.x0,\n",
" y0 = bounds.y0 - scale * bounds.y0;\n",
"\n",
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" ty = Math.max(Math.min(ty - y0, y_max), y_min);\n",
"\n",
" tx += x0;\n",
" ty += y0;\n",
"\n",
" // when the scale change, we may need to alter which set of\n",
" // ticks is being displayed\n",
" if (scale != old_scale) {\n",
" update_tickscale(root, scale, \"x\");\n",
" update_tickscale(root, scale, \"y\");\n",
" }\n",
"\n",
" set_geometry_transform(root, tx, ty, scale);\n",
"\n",
" root.data(\"scale\", scale);\n",
" root.data(\"tx\", tx);\n",
" root.data(\"ty\", ty);\n",
"};\n",
"\n",
"\n",
"var scale_centered_translation = function(root, scale) {\n",
" var bounds = root.plotbounds();\n",
"\n",
" var width = bounds.x1 - bounds.x0,\n",
" height = bounds.y1 - bounds.y0;\n",
"\n",
" var tx0 = root.data(\"tx\"),\n",
" ty0 = root.data(\"ty\");\n",
"\n",
" var scale0 = root.data(\"scale\");\n",
"\n",
" // how off from center the current view is\n",
" var xoff = tx0 - (bounds.x0 * (1 - scale0) + (width * (1 - scale0)) / 2),\n",
" yoff = ty0 - (bounds.y0 * (1 - scale0) + (height * (1 - scale0)) / 2);\n",
"\n",
" // rescale offsets\n",
" xoff = xoff * scale / scale0;\n",
" yoff = yoff * scale / scale0;\n",
"\n",
" // adjust for the panel position being scaled\n",
" var x_edge_adjust = bounds.x0 * (1 - scale),\n",
" y_edge_adjust = bounds.y0 * (1 - scale);\n",
"\n",
" return {\n",
" x: xoff + x_edge_adjust + (width - width * scale) / 2,\n",
" y: yoff + y_edge_adjust + (height - height * scale) / 2\n",
" };\n",
"};\n",
"\n",
"\n",
"// Initialize data for panning zooming if it isn't already.\n",
"var init_pan_zoom = function(root) {\n",
" if (root.data(\"zoompan-ready\")) {\n",
" return;\n",
" }\n",
"\n",
" // The non-scaling-stroke trick. Rather than try to correct for the\n",
" // stroke-width when zooming, we force it to a fixed value.\n",
" var px_per_mm = root.node.getCTM().a;\n",
"\n",
" // Drag events report deltas in pixels, which we'd like to convert to\n",
" // millimeters.\n",
" root.data(\"px_per_mm\", px_per_mm);\n",
"\n",
" root.selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" sw = element.asPX(\"stroke-width\") * px_per_mm;\n",
" if (sw > 0) {\n",
" element.attribute(\"stroke-width\", sw);\n",
" element.attribute(\"vector-effect\", \"non-scaling-stroke\");\n",
" }\n",
" });\n",
"\n",
" // Store ticks labels original tranformation\n",
" root.selectAll(\".xlabels > text, .ylabels > text\")\n",
" .forEach(function (element, i) {\n",
" var lm = element.transform().localMatrix;\n",
" element.data(\"static_transform\",\n",
" new Snap.Matrix(lm.a, lm.b, lm.c, lm.d, lm.e, lm.f));\n",
" });\n",
"\n",
" var xgridlines = root.select(\".xgridlines\");\n",
" var ygridlines = root.select(\".ygridlines\");\n",
" var xlabels = root.select(\".xlabels\");\n",
" var ylabels = root.select(\".ylabels\");\n",
"\n",
" if (root.data(\"tx\") === undefined) root.data(\"tx\", 0);\n",
" if (root.data(\"ty\") === undefined) root.data(\"ty\", 0);\n",
" if (root.data(\"scale\") === undefined) root.data(\"scale\", 1.0);\n",
" if (root.data(\"xtickscales\") === undefined) {\n",
"\n",
" // index all the tick scales that are listed\n",
" var xtickscales = {};\n",
" var ytickscales = {};\n",
" var add_x_tick_scales = function (element, i) {\n",
" xtickscales[element.attribute(\"gadfly:scale\")] = true;\n",
" };\n",
" var add_y_tick_scales = function (element, i) {\n",
" ytickscales[element.attribute(\"gadfly:scale\")] = true;\n",
" };\n",
"\n",
" if (xgridlines) xgridlines.selectAll(\"path\").forEach(add_x_tick_scales);\n",
" if (ygridlines) ygridlines.selectAll(\"path\").forEach(add_y_tick_scales);\n",
" if (xlabels) xlabels.selectAll(\"text\").forEach(add_x_tick_scales);\n",
" if (ylabels) ylabels.selectAll(\"text\").forEach(add_y_tick_scales);\n",
"\n",
" root.data(\"xtickscales\", xtickscales);\n",
" root.data(\"ytickscales\", ytickscales);\n",
" root.data(\"xtickscale\", 1.0);\n",
" }\n",
"\n",
" var min_scale = 1.0, max_scale = 1.0;\n",
" for (scale in xtickscales) {\n",
" min_scale = Math.min(min_scale, scale);\n",
" max_scale = Math.max(max_scale, scale);\n",
" }\n",
" for (scale in ytickscales) {\n",
" min_scale = Math.min(min_scale, scale);\n",
" max_scale = Math.max(max_scale, scale);\n",
" }\n",
" root.data(\"min_scale\", min_scale);\n",
" root.data(\"max_scale\", max_scale);\n",
"\n",
" // store the original positions of labels\n",
" if (xlabels) {\n",
" xlabels.selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" element.data(\"x\", element.asPX(\"x\"));\n",
" });\n",
" }\n",
"\n",
" if (ylabels) {\n",
" ylabels.selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" element.data(\"y\", element.asPX(\"y\"));\n",
" });\n",
" }\n",
"\n",
" // mark grid lines and ticks as in or out of scale.\n",
" var mark_inscale = function (element, i) {\n",
" element.attribute(\"gadfly:inscale\", element.attribute(\"gadfly:scale\") == 1.0);\n",
" };\n",
"\n",
" if (xgridlines) xgridlines.selectAll(\"path\").forEach(mark_inscale);\n",
" if (ygridlines) ygridlines.selectAll(\"path\").forEach(mark_inscale);\n",
" if (xlabels) xlabels.selectAll(\"text\").forEach(mark_inscale);\n",
" if (ylabels) ylabels.selectAll(\"text\").forEach(mark_inscale);\n",
"\n",
" // figure out the upper ond lower bounds on panning using the maximum\n",
" // and minum grid lines\n",
" var bounds = root.plotbounds();\n",
" var pan_bounds = {\n",
" x0: 0.0,\n",
" y0: 0.0,\n",
" x1: 0.0,\n",
" y1: 0.0\n",
" };\n",
"\n",
" if (xgridlines) {\n",
" xgridlines\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var bbox = element.node.getBBox();\n",
" if (bounds.x1 - bbox.x < pan_bounds.x0) {\n",
" pan_bounds.x0 = bounds.x1 - bbox.x;\n",
" }\n",
" if (bounds.x0 - bbox.x > pan_bounds.x1) {\n",
" pan_bounds.x1 = bounds.x0 - bbox.x;\n",
" }\n",
" element.attr(\"visibility\", \"visible\");\n",
" }\n",
" });\n",
" }\n",
"\n",
" if (ygridlines) {\n",
" ygridlines\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var bbox = element.node.getBBox();\n",
" if (bounds.y1 - bbox.y < pan_bounds.y0) {\n",
" pan_bounds.y0 = bounds.y1 - bbox.y;\n",
" }\n",
" if (bounds.y0 - bbox.y > pan_bounds.y1) {\n",
" pan_bounds.y1 = bounds.y0 - bbox.y;\n",
" }\n",
" element.attr(\"visibility\", \"visible\");\n",
" }\n",
" });\n",
" }\n",
"\n",
" // nudge these values a little\n",
" pan_bounds.x0 -= 5;\n",
" pan_bounds.x1 += 5;\n",
" pan_bounds.y0 -= 5;\n",
" pan_bounds.y1 += 5;\n",
" root.data(\"pan_bounds\", pan_bounds);\n",
"\n",
" root.data(\"zoompan-ready\", true)\n",
"};\n",
"\n",
"\n",
"// drag actions, i.e. zooming and panning\n",
"var pan_action = {\n",
" start: function(root, x, y, event) {\n",
" root.data(\"dx\", 0);\n",
" root.data(\"dy\", 0);\n",
" root.data(\"tx0\", root.data(\"tx\"));\n",
" root.data(\"ty0\", root.data(\"ty\"));\n",
" },\n",
" update: function(root, dx, dy, x, y, event) {\n",
" var px_per_mm = root.data(\"px_per_mm\");\n",
" dx /= px_per_mm;\n",
" dy /= px_per_mm;\n",
"\n",
" var tx0 = root.data(\"tx\"),\n",
" ty0 = root.data(\"ty\");\n",
"\n",
" var dx0 = root.data(\"dx\"),\n",
" dy0 = root.data(\"dy\");\n",
"\n",
" root.data(\"dx\", dx);\n",
" root.data(\"dy\", dy);\n",
"\n",
" dx = dx - dx0;\n",
" dy = dy - dy0;\n",
"\n",
" var tx = tx0 + dx,\n",
" ty = ty0 + dy;\n",
"\n",
" set_plot_pan_zoom(root, tx, ty, root.data(\"scale\"));\n",
" },\n",
" end: function(root, event) {\n",
"\n",
" },\n",
" cancel: function(root) {\n",
" set_plot_pan_zoom(root, root.data(\"tx0\"), root.data(\"ty0\"), root.data(\"scale\"));\n",
" }\n",
"};\n",
"\n",
"var zoom_box;\n",
"var zoom_action = {\n",
" start: function(root, x, y, event) {\n",
" var bounds = root.plotbounds();\n",
" var width = bounds.x1 - bounds.x0,\n",
" height = bounds.y1 - bounds.y0;\n",
" var ratio = width / height;\n",
" var xscalable = root.hasClass(\"xscalable\"),\n",
" yscalable = root.hasClass(\"yscalable\");\n",
" var px_per_mm = root.data(\"px_per_mm\");\n",
" x = xscalable ? x / px_per_mm : bounds.x0;\n",
" y = yscalable ? y / px_per_mm : bounds.y0;\n",
" var w = xscalable ? 0 : width;\n",
" var h = yscalable ? 0 : height;\n",
" zoom_box = root.rect(x, y, w, h).attr({\n",
" \"fill\": \"#000\",\n",
" \"opacity\": 0.25\n",
" });\n",
" zoom_box.data(\"ratio\", ratio);\n",
" },\n",
" update: function(root, dx, dy, x, y, event) {\n",
" var xscalable = root.hasClass(\"xscalable\"),\n",
" yscalable = root.hasClass(\"yscalable\");\n",
" var px_per_mm = root.data(\"px_per_mm\");\n",
" var bounds = root.plotbounds();\n",
" if (yscalable) {\n",
" y /= px_per_mm;\n",
" y = Math.max(bounds.y0, y);\n",
" y = Math.min(bounds.y1, y);\n",
" } else {\n",
" y = bounds.y1;\n",
" }\n",
" if (xscalable) {\n",
" x /= px_per_mm;\n",
" x = Math.max(bounds.x0, x);\n",
" x = Math.min(bounds.x1, x);\n",
" } else {\n",
" x = bounds.x1;\n",
" }\n",
"\n",
" dx = x - zoom_box.attr(\"x\");\n",
" dy = y - zoom_box.attr(\"y\");\n",
" if (xscalable && yscalable) {\n",
" var ratio = zoom_box.data(\"ratio\");\n",
" var width = Math.min(Math.abs(dx), ratio * Math.abs(dy));\n",
" var height = Math.min(Math.abs(dy), Math.abs(dx) / ratio);\n",
" dx = width * dx / Math.abs(dx);\n",
" dy = height * dy / Math.abs(dy);\n",
" }\n",
" var xoffset = 0,\n",
" yoffset = 0;\n",
" if (dx < 0) {\n",
" xoffset = dx;\n",
" dx = -1 * dx;\n",
" }\n",
" if (dy < 0) {\n",
" yoffset = dy;\n",
" dy = -1 * dy;\n",
" }\n",
" if (isNaN(dy)) {\n",
" dy = 0.0;\n",
" }\n",
" if (isNaN(dx)) {\n",
" dx = 0.0;\n",
" }\n",
" zoom_box.transform(\"T\" + xoffset + \",\" + yoffset);\n",
" zoom_box.attr(\"width\", dx);\n",
" zoom_box.attr(\"height\", dy);\n",
" },\n",
" end: function(root, event) {\n",
" var xscalable = root.hasClass(\"xscalable\"),\n",
" yscalable = root.hasClass(\"yscalable\");\n",
" var zoom_bounds = zoom_box.getBBox();\n",
" if (zoom_bounds.width * zoom_bounds.height <= 0) {\n",
" return;\n",
" }\n",
" var plot_bounds = root.plotbounds();\n",
" var zoom_factor = 1.0;\n",
" if (yscalable) {\n",
" zoom_factor = (plot_bounds.y1 - plot_bounds.y0) / zoom_bounds.height;\n",
" } else {\n",
" zoom_factor = (plot_bounds.x1 - plot_bounds.x0) / zoom_bounds.width;\n",
" }\n",
" var tx = (root.data(\"tx\") - zoom_bounds.x) * zoom_factor + plot_bounds.x0,\n",
" ty = (root.data(\"ty\") - zoom_bounds.y) * zoom_factor + plot_bounds.y0;\n",
" set_plot_pan_zoom(root, tx, ty, root.data(\"scale\") * zoom_factor);\n",
" zoom_box.remove();\n",
" },\n",
" cancel: function(root) {\n",
" zoom_box.remove();\n",
" }\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_drag_onstart = function(x, y, event) {\n",
" var root = this.plotroot();\n",
" var scalable = root.hasClass(\"xscalable\") || root.hasClass(\"yscalable\");\n",
" var zoomable = !event.altKey && !event.ctrlKey && event.shiftKey && scalable;\n",
" var panable = !event.altKey && !event.ctrlKey && !event.shiftKey && scalable;\n",
" var drag_action = zoomable ? zoom_action :\n",
" panable ? pan_action :\n",
" undefined;\n",
" root.data(\"drag_action\", drag_action);\n",
" if (drag_action) {\n",
" var cancel_drag_action = function(event) {\n",
" if (event.which == 27) { // esc key\n",
" drag_action.cancel(root);\n",
" root.data(\"drag_action\", undefined);\n",
" }\n",
" };\n",
" window.addEventListener(\"keyup\", cancel_drag_action);\n",
" root.data(\"cancel_drag_action\", cancel_drag_action);\n",
" drag_action.start(root, x, y, event);\n",
" }\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_drag_onmove = function(dx, dy, x, y, event) {\n",
" var root = this.plotroot();\n",
" var drag_action = root.data(\"drag_action\");\n",
" if (drag_action) {\n",
" drag_action.update(root, dx, dy, x, y, event);\n",
" }\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_drag_onend = function(event) {\n",
" var root = this.plotroot();\n",
" window.removeEventListener(\"keyup\", root.data(\"cancel_drag_action\"));\n",
" root.data(\"cancel_drag_action\", undefined);\n",
" var drag_action = root.data(\"drag_action\");\n",
" if (drag_action) {\n",
" drag_action.end(root, event);\n",
" }\n",
" root.data(\"drag_action\", undefined);\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_scroll = function(event) {\n",
" if (event.shiftKey) {\n",
" increase_zoom_by_position(this.plotroot(), 0.001 * event.wheelDelta);\n",
" event.preventDefault();\n",
" }\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_button_mouseover = function(event) {\n",
" this.select(\".button_logo\")\n",
" .animate({fill: this.data(\"mouseover_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_button_mouseout = function(event) {\n",
" this.select(\".button_logo\")\n",
" .animate({fill: this.data(\"mouseout_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_zoomout_click = function(event) {\n",
" increase_zoom_by_position(this.plotroot(), -0.1, true);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_zoomin_click = function(event) {\n",
" increase_zoom_by_position(this.plotroot(), 0.1, true);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_track_click = function(event) {\n",
" // TODO\n",
"};\n",
"\n",
"\n",
"// Map slider position x to scale y using the function y = a*exp(b*x)+c.\n",
"// The constants a, b, and c are solved using the constraint that the function\n",
"// should go through the points (0; min_scale), (0.5; 1), and (1; max_scale).\n",
"var scale_from_slider_position = function(position, min_scale, max_scale) {\n",
" var a = (1 - 2 * min_scale + min_scale * min_scale) / (min_scale + max_scale - 2),\n",
" b = 2 * Math.log((max_scale - 1) / (1 - min_scale)),\n",
" c = (min_scale * max_scale - 1) / (min_scale + max_scale - 2);\n",
" return a * Math.exp(b * position) + c;\n",
"}\n",
"\n",
"// inverse of scale_from_slider_position\n",
"var slider_position_from_scale = function(scale, min_scale, max_scale) {\n",
" var a = (1 - 2 * min_scale + min_scale * min_scale) / (min_scale + max_scale - 2),\n",
" b = 2 * Math.log((max_scale - 1) / (1 - min_scale)),\n",
" c = (min_scale * max_scale - 1) / (min_scale + max_scale - 2);\n",
" return 1 / b * Math.log((scale - c) / a);\n",
"}\n",
"\n",
"var increase_zoom_by_position = function(root, delta_position, animate) {\n",
" var scale = root.data(\"scale\"),\n",
" min_scale = root.data(\"min_scale\"),\n",
" max_scale = root.data(\"max_scale\");\n",
" var position = slider_position_from_scale(scale, min_scale, max_scale);\n",
" position += delta_position;\n",
" scale = scale_from_slider_position(position, min_scale, max_scale);\n",
" set_zoom(root, scale, animate);\n",
"}\n",
"\n",
"var set_zoom = function(root, scale, animate) {\n",
" var min_scale = root.data(\"min_scale\"),\n",
" max_scale = root.data(\"max_scale\"),\n",
" old_scale = root.data(\"scale\");\n",
" var new_scale = Math.max(min_scale, Math.min(scale, max_scale));\n",
" if (animate) {\n",
" Snap.animate(\n",
" old_scale,\n",
" new_scale,\n",
" function (new_scale) {\n",
" update_plot_scale(root, new_scale);\n",
" },\n",
" 200);\n",
" } else {\n",
" update_plot_scale(root, new_scale);\n",
" }\n",
"}\n",
"\n",
"\n",
"var update_plot_scale = function(root, new_scale) {\n",
" var trans = scale_centered_translation(root, new_scale);\n",
" set_plot_pan_zoom(root, trans.x, trans.y, new_scale);\n",
"\n",
" root.selectAll(\".zoomslider_thumb\")\n",
" .forEach(function (element, i) {\n",
" var min_pos = element.data(\"min_pos\"),\n",
" max_pos = element.data(\"max_pos\"),\n",
" min_scale = root.data(\"min_scale\"),\n",
" max_scale = root.data(\"max_scale\");\n",
" var xmid = (min_pos + max_pos) / 2;\n",
" var xpos = slider_position_from_scale(new_scale, min_scale, max_scale);\n",
" element.transform(new Snap.Matrix().translate(\n",
" Math.max(min_pos, Math.min(\n",
" max_pos, min_pos + (max_pos - min_pos) * xpos)) - xmid, 0));\n",
" });\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_dragmove = function(dx, dy, x, y, event) {\n",
" var root = this.plotroot();\n",
" var min_pos = this.data(\"min_pos\"),\n",
" max_pos = this.data(\"max_pos\"),\n",
" min_scale = root.data(\"min_scale\"),\n",
" max_scale = root.data(\"max_scale\"),\n",
" old_scale = root.data(\"old_scale\");\n",
"\n",
" var px_per_mm = root.data(\"px_per_mm\");\n",
" dx /= px_per_mm;\n",
" dy /= px_per_mm;\n",
"\n",
" var xmid = (min_pos + max_pos) / 2;\n",
" var xpos = slider_position_from_scale(old_scale, min_scale, max_scale) +\n",
" dx / (max_pos - min_pos);\n",
"\n",
" // compute the new scale\n",
" var new_scale = scale_from_slider_position(xpos, min_scale, max_scale);\n",
" new_scale = Math.min(max_scale, Math.max(min_scale, new_scale));\n",
"\n",
" update_plot_scale(root, new_scale);\n",
" event.stopPropagation();\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_dragstart = function(x, y, event) {\n",
" this.animate({fill: this.data(\"mouseover_color\")}, 100);\n",
" var root = this.plotroot();\n",
"\n",
" // keep track of what the scale was when we started dragging\n",
" root.data(\"old_scale\", root.data(\"scale\"));\n",
" event.stopPropagation();\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_dragend = function(event) {\n",
" this.animate({fill: this.data(\"mouseout_color\")}, 100);\n",
" event.stopPropagation();\n",
"};\n",
"\n",
"\n",
"var toggle_color_class = function(root, color_class, ison) {\n",
" var guides = root.selectAll(\".guide.\" + color_class + \",.guide .\" + color_class);\n",
" var geoms = root.selectAll(\".geometry.\" + color_class + \",.geometry .\" + color_class);\n",
" if (ison) {\n",
" guides.animate({opacity: 0.5}, 250);\n",
" geoms.animate({opacity: 0.0}, 250);\n",
" } else {\n",
" guides.animate({opacity: 1.0}, 250);\n",
" geoms.animate({opacity: 1.0}, 250);\n",
" }\n",
"};\n",
"\n",
"\n",
"Gadfly.colorkey_swatch_click = function(event) {\n",
" var root = this.plotroot();\n",
" var color_class = this.data(\"color_class\");\n",
"\n",
" if (event.shiftKey) {\n",
" root.selectAll(\".colorkey text\")\n",
" .forEach(function (element) {\n",
" var other_color_class = element.data(\"color_class\");\n",
" if (other_color_class != color_class) {\n",
" toggle_color_class(root, other_color_class,\n",
" element.attr(\"opacity\") == 1.0);\n",
" }\n",
" });\n",
" } else {\n",
" toggle_color_class(root, color_class, this.attr(\"opacity\") == 1.0);\n",
" }\n",
"};\n",
"\n",
"\n",
"return Gadfly;\n",
"\n",
"}));\n",
"\n",
"\n",
"//@ sourceURL=gadfly.js\n",
"\n",
"(function (glob, factory) {\n",
" // AMD support\n",
" if (typeof require === \"function\" && typeof define === \"function\" && define.amd) {\n",
" require([\"Snap.svg\", \"Gadfly\"], function (Snap, Gadfly) {\n",
" factory(Snap, Gadfly);\n",
" });\n",
" } else {\n",
" factory(glob.Snap, glob.Gadfly);\n",
" }\n",
"})(window, function (Snap, Gadfly) {\n",
" var fig = Snap(\"#img-9c166513\");\n",
"fig.select(\"#img-9c166513-5\")\n",
" .init_gadfly();\n",
"fig.select(\"#img-9c166513-7\")\n",
" .plotroot().data(\"unfocused_ygrid_color\", \"#D0D0E0\")\n",
";\n",
"fig.select(\"#img-9c166513-7\")\n",
" .plotroot().data(\"focused_ygrid_color\", \"#A0A0A0\")\n",
";\n",
"fig.select(\"#img-9c166513-8\")\n",
" .plotroot().data(\"unfocused_xgrid_color\", \"#D0D0E0\")\n",
";\n",
"fig.select(\"#img-9c166513-8\")\n",
" .plotroot().data(\"focused_xgrid_color\", \"#A0A0A0\")\n",
";\n",
"fig.select(\"#img-9c166513-20\")\n",
" .data(\"mouseover_color\", \"#CD5C5C\")\n",
";\n",
"fig.select(\"#img-9c166513-20\")\n",
" .data(\"mouseout_color\", \"#6A6A6A\")\n",
";\n",
"fig.select(\"#img-9c166513-20\")\n",
" .click(Gadfly.zoomslider_zoomin_click)\n",
".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
";\n",
"fig.select(\"#img-9c166513-22\")\n",
" .data(\"max_pos\", 79)\n",
";\n",
"fig.select(\"#img-9c166513-22\")\n",
" .data(\"min_pos\", 62)\n",
";\n",
"fig.select(\"#img-9c166513-22\")\n",
" .click(Gadfly.zoomslider_track_click);\n",
"fig.select(\"#img-9c166513-23\")\n",
" .data(\"max_pos\", 79)\n",
";\n",
"fig.select(\"#img-9c166513-23\")\n",
" .data(\"min_pos\", 62)\n",
";\n",
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";\n",
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";\n",
"fig.select(\"#img-9c166513-23\")\n",
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";\n",
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";\n",
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";\n",
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"</svg>\n"
],
"text/plain": [
"Plot(...)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"el = Seg3([1, 2, 3])\n",
"el[\"geometry\"] = Node[[-0.2, -0.1], [1.0, 0.8], [0.2, 0.7]]\n",
"x = Float64[]\n",
"y = Float64[]\n",
"for xi in linspace(-1, 1)\n",
" X = el(\"geometry\", [xi], 0.0)\n",
" push!(x, X[1])\n",
" push!(y, X[2])\n",
"end\n",
"l1 = layer(x=x, y=y, Geom.line)\n",
"\n",
"X1 = el(\"geometry\", [-1.0], 0.0)\n",
"X2 = el(\"geometry\", [1.0], 0.0)\n",
"X3 = el(\"geometry\", [0.0], 0.0)\n",
"l2 = layer(x=[X1[1],X2[1],X3[1]], y=[X1[2],X2[2],X3[2]], label=[\"1\",\"2\",\"3\"],\n",
" Geom.point, Geom.label(;hide_overlaps=false))\n",
"\n",
"xi = [-0.5]\n",
"X = el(\"geometry\", xi, 0.0)\n",
"J = JuliaFEM.Core.get_jacobian(el, xi, 0.0)\n",
"t = vec(J)/norm(J)\n",
"n = [cos(pi/2) -sin(pi/2); sin(pi/2) cos(pi/2)]*t\n",
"a = 0.3\n",
"l3 = layer(x=[X[1], X[1]+a*t[1]], y=[X[2], X[2]+a*t[2]], label=[\"\",\"t\"],\n",
" Geom.label(;hide_overlaps=false), Geom.line, Theme(default_color=colorant\"red\"))\n",
"l4 = layer(x=[X[1], X[1]+a*n[1]], y=[X[2], X[2]+a*n[2]], label=[\"\",\"n\"],\n",
" Geom.label(;hide_overlaps=false), Geom.line, Theme(default_color=colorant\"red\"))\n",
"\n",
"p = plot(l1, l2, l3, l4, Coord.Cartesian(xmin=-0.5, ymin=-0.5, xmax=1.0, ymax=1.0))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model defined in cartesian coordinates"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Model defined using cartesian coordinates. In general set individual components of vector values using index number, 1=x, 2=y, 3=z."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO: Starting solver simple 2d block\n",
"INFO: # of field problems: 1\n",
"INFO: # of boundary problems: 1\n",
"INFO: Starting iteration 1\n",
"INFO: Assembling field problems...\n",
"INFO: Assembling body 1: block\n",
"INFO: dim = 8\n",
"INFO: Assembling boundary problems...\n",
"INFO: Assembling boundary 1: dirichlet boundary conditions\n",
"INFO: Solving system\n",
"INFO: UMFPACK: solved in 0.20885300636291504 seconds. norm = 0.16197088596792505\n"
]
},
{
"data": {
"text/plain": [
"(1,true)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO: timing info for iteration:\n",
"INFO: boundary assembly : 0.11499595642089844\n",
"INFO: field assembly : 1.344099998474121\n",
"INFO: dump matrices to disk : 1.1920928955078125e-6\n",
"INFO: solve problem : 0.38971495628356934\n",
"INFO: update element data : 0.031152963638305664\n",
"INFO: non-linear iteration : 1.879986047744751\n",
"INFO: solver finished in 2.0280649662017822 seconds.\n"
]
}
],
"source": [
"geometry = Dict{Int64, Node}(\n",
" 1 => [0.0, 0.0],\n",
" 2 => [1.0, 0.0],\n",
" 3 => [1.0, 1.0],\n",
" 4 => [0.0, 1.0])\n",
"el1 = Quad4([1, 2, 3, 4])\n",
"el2 = Seg2([3, 4]) # load\n",
"el3 = Seg2([1, 2]) # symmetry 2\n",
"el4 = Seg2([4, 1]) # symmetry 1\n",
"update!([el1, el2, el3, el4], \"geometry\", geometry)\n",
"el1[\"youngs modulus\"] = 900.0\n",
"el1[\"poissons ratio\"] = 0.25\n",
"el2[\"displacement traction force 2\"] = -100.0\n",
"el3[\"displacement 2\"] = 0.0\n",
"el4[\"displacement 1\"] = 0.0\n",
"problem = PlaneStressLinearElasticityProblem(\"block\")\n",
"boundary = DirichletProblem(\"dirichlet boundary conditions\", \"displacement\", 2)\n",
"push!(problem, el1, el2)\n",
"push!(boundary, el3, el4)\n",
"solver = DirectSolver(\"simple 2d block\")\n",
"push!(solver, problem)\n",
"push!(solver, boundary)\n",
"solver.method = :UMFPACK\n",
"solver.nonlinear_problem = false\n",
"call(solver, 0.0)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"Test Passed\n",
" Expression: isapprox(el1(\"displacement\",[1.0,1.0],0.0),[1 / 36,-1 / 9])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using JuliaFEM.Test\n",
"@test isapprox(el1(\"displacement\", [1.0, 1.0], 0.0), [1/36, -1/9])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.11453071182271282"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm(el1(\"displacement\", [1.0, 1.0], 0.0))"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
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"d})};a.filter.saturate.toString=function(){return this()};a.filter.hueRotate=function(d){return a.format('<feColorMatrix type=\"hueRotate\" values=\"{angle}\"/>',{angle:d||0})};a.filter.hueRotate.toString=function(){return this()};a.filter.invert=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"table\" tableValues=\"{amount} {amount2}\"/><feFuncG type=\"table\" tableValues=\"{amount} {amount2}\"/><feFuncB type=\"table\" tableValues=\"{amount} {amount2}\"/></feComponentTransfer>',{amount:d,\n",
"amount2:1-d})};a.filter.invert.toString=function(){return this()};a.filter.brightness=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\"/><feFuncG type=\"linear\" slope=\"{amount}\"/><feFuncB type=\"linear\" slope=\"{amount}\"/></feComponentTransfer>',{amount:d})};a.filter.brightness.toString=function(){return this()};a.filter.contrast=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncG type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncB type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/></feComponentTransfer>',\n",
"{amount:d,amount2:0.5-d/2})};a.filter.contrast.toString=function(){return this()}});return C});\n",
"\n",
"]]> </script>\n",
"</svg>\n"
],
"text/plain": [
"Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:cx,Int64},Measures.Length{:cy,Int64}},Tuple{Measures.Length{:cx,Int64},Measures.Length{:cy,Int64}}}((0cx,0cy),(1cx,1cy)),Nullable{Compose.UnitBox{S,T,U,V}}(),Nullable{Compose.Rotation{P<:NTuple{N,Measures.Measure}}}(),Nullable{Compose.Mirror}(),Compose.ListNode{Compose.Container}(Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:cx,Int64},Measures.Length{:cy,Int64}},Tuple{Measures.Length{:cx,Int64},Measures.Length{:cy,Int64}}}((0cx,0cy),(1cx,1cy)),Nullable{Compose.UnitBox{S,T,U,V}}(),Nullable{Compose.Rotation{P<:NTuple{N,Measures.Measure}}}(),Nullable{Compose.Mirror}(),Compose.ListNull{Compose.Container}(),Compose.ListNode{Compose.Form{P<:Compose.FormPrimitive}}(Compose.Form{Compose.SimplePolygonPrimitive{Tuple{Measures.Length{:cx,Float64},Measures.Length{:cy,Float64}}}}([Compose.SimplePolygonPrimitive{Tuple{Measures.Length{:cx,Float64},Measures.Length{:cy,Float64}}}([(0.0cx,0.0cy),(1.0277777777777777cx,0.0cy),(1.0277777777777777cx,0.8888888888888888cy),(0.0cx,0.8888888888888888cy)])],symbol(\"\")),Compose.ListNull{Compose.Form{P<:Compose.FormPrimitive}}()),Compose.ListNode{Compose.Property{P<:Compose.PropertyPrimitive}}(Compose.Property{Compose.StrokePrimitive}([Compose.StrokePrimitive(RGBA{Float64}(1.0,0.0,0.0,1.0))]),Compose.ListNode{Compose.Property{P<:Compose.PropertyPrimitive}}(Compose.Property{Compose.FillPrimitive}([Compose.FillPrimitive(RGBA{Float64}(0.0,0.0,0.0,0.0))]),Compose.ListNode{Compose.Property{P<:Compose.PropertyPrimitive}}(Compose.Property{Compose.LineWidthPrimitive}([Compose.LineWidthPrimitive(1.0mm)]),Compose.ListNull{Compose.Property{P<:Compose.PropertyPrimitive}}()))),0,false,false,false,false,nothing,nothing,0.0,symbol(\"\")),Compose.ListNull{Compose.Container}()),Compose.ListNode{Compose.Form{P<:Compose.FormPrimitive}}(Compose.Form{Compose.SimplePolygonPrimitive{Tuple{Measures.Length{:cx,Float64},Measures.Length{:cy,Float64}}}}([Compose.SimplePolygonPrimitive{Tuple{Measures.Length{:cx,Float64},Measures.Length{:cy,Float64}}}([(0.0cx,0.0cy),(1.0cx,0.0cy),(1.0cx,1.0cy),(0.0cx,1.0cy)])],symbol(\"\")),Compose.ListNull{Compose.Form{P<:Compose.FormPrimitive}}()),Compose.ListNode{Compose.Property{P<:Compose.PropertyPrimitive}}(Compose.Property{Compose.StrokePrimitive}([Compose.StrokePrimitive(RGBA{Float64}(0.0,0.0,0.0,1.0))]),Compose.ListNode{Compose.Property{P<:Compose.PropertyPrimitive}}(Compose.Property{Compose.FillPrimitive}([Compose.FillPrimitive(RGBA{Float64}(0.0,0.0,0.0,0.0))]),Compose.ListNode{Compose.Property{P<:Compose.PropertyPrimitive}}(Compose.Property{Compose.LineWidthPrimitive}([Compose.LineWidthPrimitive(1.0mm)]),Compose.ListNull{Compose.Property{P<:Compose.PropertyPrimitive}}()))),0,false,false,false,false,nothing,nothing,0.0,symbol(\"\"))"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Compose\n",
"\n",
"X = el1(\"geometry\")\n",
"u = el1(\"displacement\", 0.0)\n",
"x = X+u\n",
"\n",
"root = context(0, 0, 1, 1)\n",
"p1 = polygon([tuple(X[i][1], X[i][2]) for i=1:4])\n",
"p2 = polygon([tuple(x[i][1], x[i][2]) for i=1:4])\n",
"undeformed = compose(root, p1, linewidth(1mm), fill(nothing), stroke(\"black\"))\n",
"deformed = compose(root, p2, linewidth(1mm), fill(nothing), stroke(\"red\"))\n",
"compose(undeformed, deformed)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Using normal tangential coordinates\n",
"\n",
"Sometimes it's more convenient to set boundary conditions using normal-tangential coordinates."
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"rot (generic function with 1 method)"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rot(ϕ) = [cos(ϕ) -sin(ϕ); sin(ϕ) cos(ϕ)]"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"false"
]
},
"execution_count": 84,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using JuliaFEM.Core: Quad4, Seg2, Seg3, PlaneStressLinearElasticityProblem, DirichletProblem, update!, DirectSolver\n",
"typealias Node Vector{Float64}\n",
"using JuliaFEM.Core: calculate_normal_tangential_coordinates!\n",
"\n",
"# 2d rotation matrix\n",
"#phi = pi/10\n",
"phi = 0.0\n",
"rmat(phi) = [cos(phi) -sin(phi); sin(phi) cos(phi)]\n",
"\n",
"geometry = Dict{Int64, Node}(\n",
" 1 => rmat(phi)*[0.0, 0.0],\n",
" 2 => rmat(phi)*[1.0, 0.0],\n",
" 3 => rmat(phi)*[1.0, 1.0],\n",
" 4 => rmat(phi)*[0.0, 1.0])\n",
"el1 = Quad4([1, 2, 3, 4])\n",
"el2 = Seg2([3, 4]) # load\n",
"el3 = Seg2([1, 2]) # symmetry 2\n",
"el4 = Seg2([4, 1]) # symmetry 1\n",
"update!([el1, el2, el3, el4], \"geometry\", geometry)\n",
"calculate_normal_tangential_coordinates!([el2, el3, el4], 0.0)\n",
"\n",
"el1[\"youngs modulus\"] = 900.0\n",
"el1[\"poissons ratio\"] = 0.25\n",
"# traction force in local coordinates\n",
"el2[\"local displacement traction force 1\"] = 100.0\n",
"# support sides in local coordinates\n",
"el3[\"local displacement 1\"] = 0.0\n",
"el4[\"local displacement 2\"] = 0.0\n",
"for el in [el3, el4]\n",
" el[\"displacement near coord (0.0,0.0)\"] = 0.0\n",
"end\n",
"problem = PlaneStressLinearElasticityProblem(\"block\")\n",
"boundary = DirichletProblem(\"dirichlet boundary conditions\", \"displacement\", 2)\n",
"push!(problem, el1, el2)\n",
"push!(boundary, el3, el4)\n",
"solver = DirectSolver(\"rotated 2d block\")\n",
"push!(solver, problem)\n",
"push!(solver, boundary)\n",
"solver.method = :UMFPACK\n",
"solver.nonlinear_problem = false\n",
"#call(solver, 0.0)"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"8x1 sparse matrix with 2 Float64 entries:\n",
"\t[6, 1] = -50.0\n",
"\t[8, 1] = -50.0"
]
},
"execution_count": 85,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"K = sparse(JuliaFEM.Core.assemble(problem, 0.0).stiffness_matrix)\n",
"f = sparse(JuliaFEM.Core.assemble(problem, 0.0).force_vector)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"using JuliaFEM.Core: SparseMatrixCOO\n",
"\n",
"\"\"\"\n",
"For general problem type\n",
"Au + C₁'λ = f\n",
"C₂u + Dλ = g\n",
"\"\"\"\n",
"type BoundaryAssembly\n",
" C1 :: SparseMatrixCOO\n",
" C2 :: SparseMatrixCOO\n",
" D :: SparseMatrixCOO\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"BoundaryAssembly"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function BoundaryAssembly()\n",
" return BoundaryAssembly(SparseMatrixCOO(), SparseMatrixCOO(), SparseMatrixCOO())\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO: De = [0.5 0.0\n",
" 0.0 0.5]\n",
"INFO: De = [0.5 0.0\n",
" 0.0 0.5]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Array(Float64,(8,8)) 8x8 Array{Float64,2}"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO: De = [0.5 0.0\n",
" 0.0 0.5]\n",
"INFO: De = [0.5 0.0\n",
" 0.0 0.5]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
":\n",
" 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0\n",
"Array(Float64,(7,8)) 7x8 Array{Float64,2}:\n",
" 2.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 2.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 2.0 0.0\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 2.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 2.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.0\n"
]
}
],
"source": [
"using JuliaFEM.Core: get_gdofs, get_integration_points, get_jacobian, add!, get_connectivity\n",
"\n",
"function do_boundary()\n",
" assembly = BoundaryAssembly()\n",
" field_dim = 2\n",
" time = 0.0\n",
" for element in [el3, el4]\n",
" gdofs = get_gdofs(element, field_dim)\n",
" for ip in get_integration_points(element, Val{2})\n",
" w = ip.weight\n",
" J = get_jacobian(element, ip, time)\n",
" N = element(ip, time)\n",
" N_bo = [1/2*(1-3*ip.xi[1]) 1/2*(1+3*ip.xi[1])]\n",
" #C1 = w*N_bo'*N*norm(J)\n",
" De = eye(2)*norm(J)\n",
" info(\"De = $De\")\n",
" # add to C1\n",
" for i=1:field_dim\n",
" ldofs = gdofs[i:field_dim:end]\n",
" add!(assembly.C1, ldofs, ldofs, De)\n",
" end\n",
" # add to C2\n",
" nt = element(\"normal-tangential coordinates\", ip, time)\n",
" nt = transpose(nt)\n",
" normal = nt[1,:]\n",
" tangent = nt[2,:]\n",
" for nid in get_connectivity(element)\n",
" ndofs = [2*(nid-1)+1, 2*(nid-1)+2]\n",
" add!(assembly.C2, [2*(nid-1)+1], ndofs, normal)\n",
" add!(assembly.D, [2*(nid-1)+2], ndofs, tangent)\n",
" end\n",
" end\n",
" end\n",
" return assembly\n",
"end\n",
"\n",
"ntass = do_boundary()\n",
"ENV[\"COLUMNS\"] = 300\n",
"dump(round(full(ntass.C1), 2))\n",
"dump(round(full(ntass.C2), 2))\n",
"dump(round(full(ntass.D), 2))"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO: size of A = (16,16)\n",
"INFO: total dim = 16\n"
]
},
{
"data": {
"text/plain": [
"2x8 Array{Float64,2}:\n",
" 0.0 0.0277778 0.0277778 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 -0.111111 -0.111111 -25.0 -25.0 0.0 0.0"
]
},
"execution_count": 98,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO: solving\n",
"INFO: solved\n"
]
}
],
"source": [
"g = spzeros(8, 1)\n",
"A = [K B'; C D]\n",
"b = [f; g]\n",
"\n",
"info(\"size of A = $(size(A))\")\n",
"ENV[\"COLUMNS\"] = 300\n",
"\n",
"dim = size(A, 1)\n",
"info(\"total dim = $dim\")\n",
"\n",
"nz1 = sort(unique(rowvals(A)))\n",
"nz2 = sort(unique(rowvals(A')))\n",
"A = A[nz1, nz2]\n",
"b = b[nz1]\n",
"u = zeros(dim)\n",
"T = full(A)\n",
"T[abs(T) .< 1.0e-9] = 0\n",
"info(\"solving\")\n",
"sol = T \\ full(b)\n",
"info(\"solved\")\n",
"\n",
"u[nz1] = sol\n",
"u[abs(u).<1.0e-9] = 0.0\n",
"u = reshape(full(u), 2, round(Int, length(u)/2))\n",
"full(u)"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"2-element Array{Float64,1}:\n",
" 0.0277778\n",
" -0.111111 "
]
},
"execution_count": 87,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"u[:,3]"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"Test Passed\n",
" Expression: isapprox(norm(u[:,3]),0.11453071182271282)"
]
},
"execution_count": 88,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@test isapprox(norm(u[:,3]), 0.11453071182271282)"
]
},
{
"cell_type": "code",
"execution_count": 89,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"16x16 Array{Int64,2}:\n",
" 440 150 -260 -30 -220 -150 40 30 2 0 0 0 0 0 0 0\n",
" 150 440 30 40 -150 -220 -30 -260 0 2 0 0 0 0 0 0\n",
" -260 30 440 -150 40 -30 -220 150 0 0 2 0 0 0 0 0\n",
" -30 40 -150 440 30 -260 150 -220 0 0 0 2 0 0 0 0\n",
" -220 -150 40 30 440 150 -260 -30 0 0 0 0 2 0 0 0\n",
" -150 -220 -30 -260 150 440 30 40 0 0 0 0 0 2 0 0\n",
" 40 -30 -220 150 -260 30 440 -150 0 0 0 0 0 0 2 0\n",
" 30 -260 150 -220 -30 40 -150 440 0 0 0 0 0 0 0 2\n",
" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
" 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
" 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0\n",
" 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0\n",
" 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1"
]
},
"execution_count": 89,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"round(Int, T)"
]
},
{
"cell_type": "code",
"execution_count": 119,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"16x16 Array{Float64,2}:\n",
" 440.0 150.0 -260.0 -30.0 -220.0 -150.0 40.0 30.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 150.0 440.0 30.0 40.0 -150.0 -220.0 -30.0 -260.0 0.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" -260.0 30.0 440.0 -150.0 40.0 -30.0 -220.0 150.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0\n",
" -30.0 40.0 -150.0 440.0 30.0 -260.0 150.0 -220.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0\n",
" -220.0 -150.0 40.0 30.0 440.0 150.0 -260.0 -30.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" -150.0 -220.0 -30.0 -260.0 150.0 440.0 30.0 40.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 40.0 -30.0 -220.0 150.0 -260.0 30.0 440.0 -150.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0\n",
" 30.0 -260.0 150.0 -220.0 -30.0 40.0 -150.0 440.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0\n",
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.0"
]
},
"execution_count": 119,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"C1 = sparse(ntass.C1, 8, 8)\n",
"C2 = sparse(ntass.C2, 8, 8)\n",
"D = sparse(ntass.D, 8, 8)\n",
"C2[1,:] = 0\n",
"D[2,:] = 0\n",
"C2[1,1] = 1\n",
"C2[2,2] = 1\n",
"#C2[2,:] = D[2,:]\n",
"#D[2,:] = 0\n",
"A = [K C1'; C2 D]\n",
"#A[9,:] = 0\n",
"#A[9, 1] = 1\n",
"#A[10,:] = 0\n",
"#A[10, 1] = 2\n",
"#A[10, 2] = -2\n",
"full(A)"
]
},
{
"cell_type": "code",
"execution_count": 120,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"2x8 Array{Float64,2}:\n",
" 0.0 0.0277778 0.0277778 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 -0.111111 -0.111111 -25.0 -50.0 0.0 0.0"
]
},
"execution_count": 120,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"b = [f; spzeros(8, 1)]\n",
"nz1 = sort(unique(rowvals(A)))\n",
"nz2 = sort(unique(rowvals(A')))\n",
"sol = zeros(length(b))\n",
"sol[nz1] = A[nz1, nz2] \\ full(b)[nz1]\n",
"sol[abs(sol) .< 1.0e-9] = 0\n",
"sol = reshape(sol, 2, 8)"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"Test Passed\n",
" Expression: isapprox(norm(sol[:,3]),0.11453071182271282)"
]
},
"execution_count": 83,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@test isapprox(norm(sol[:,3]), 0.11453071182271282)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"ename": "LoadError",
"evalue": "LoadError: KeyError: displacement not found\nwhile loading In[13], in expression starting on line 1",
"output_type": "error",
"traceback": [
"LoadError: KeyError: displacement not found\nwhile loading In[13], in expression starting on line 1",
"",
" in getindex at /home/jukka/.julia/v0.4/JuliaFEM/src/elements.jl:94",
" in call at /home/jukka/.julia/v0.4/JuliaFEM/src/elements.jl:130 (repeats 2 times)"
]
}
],
"source": [
"u_tip = el1(\"displacement\", [1.0, 1.0], 0.0)\n",
"info(\"displacement on tip: $u_tip, magnitude = $(norm(u_tip))\")"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error During Test\n",
" Test threw an exception of type UndefVarError\n",
" Expression: isapprox("
]
},
{
"ename": "LoadError",
"evalue": "LoadError: There was an error during testing\nwhile loading In[14], in expression starting on line 2",
"output_type": "error",
"traceback": [
"LoadError: There was an error during testing\nwhile loading In[14], in expression starting on line 2",
"",
" in record at /home/jukka/.julia/v0.4/BaseTestNext/src/BaseTestNext.jl:290",
" in do_test at /home/jukka/.julia/v0.4/BaseTestNext/src/BaseTestNext.jl:192"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"norm(u_tip),norm([1 / 36,-1 / 9]))\n",
" UndefVarError: u_tip not defined\n",
" in anonymous at /home/jukka/.julia/v0.4/BaseTestNext/src/BaseTestNext.jl:165\n",
" in do_test at /home/jukka/.julia/v0.4/BaseTestNext/src/BaseTestNext.jl:181\n",
" in include_string at loading.jl:266\n",
" in execute_request_0x535c5df2 at /home/jukka/.julia/v0.4/IJulia/src/execute_request.jl:177\n",
" in eventloop at /home/jukka/.julia/v0.4/IJulia/src/IJulia.jl:141\n",
" in anonymous at task.jl:447\n"
]
}
],
"source": [
"using JuliaFEM.Test\n",
"@test isapprox(norm(u_tip), norm([1/36, -1/9]))"
]
},
{
"cell_type": "code",
"execution_count": 108,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"using JuliaFEM.Core: Seg2, Element, update!\n",
"using JuliaFEM.Core: calculate_normal_tangential_coordinates!\n",
"typealias Node Vector{Float64}\n",
"\n",
"nodes = Dict{Int, Node}(\n",
"1 => [0.0, 0.1],\n",
"2 => [1.0, 0.3],\n",
"3 => [2.0, -0.1],\n",
"4 => [3.0, 0.6],\n",
"5 => [4.0, 0.3])\n",
"\n",
"s1 = Seg2([1, 2])\n",
"s2 = Seg2([2, 3])\n",
"s3 = Seg2([3, 4])\n",
"s4 = Seg2([4, 5])\n",
"elems = Element[s1, s2, s3, s4]\n",
"update!(elems, \"geometry\", nodes)\n",
"calculate_normal_tangential_coordinates!([s1, s2, s3, s4], 0.0)"
]
},
{
"cell_type": "code",
"execution_count": 109,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f32fdd9d5d0>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"(-0.5,4.5)"
]
},
"execution_count": 109,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using PyPlot\n",
"fig = figure(figsize=(5, 3))\n",
"for s in [s1, s2, s3, s4]\n",
" X1 = s(\"geometry\", [-1.0], 0.0)\n",
" X2 = s(\"geometry\", [ 1.0], 0.0)\n",
" nt1 = s(\"normal-tangential coordinates\", [-1.0], 0.0)\n",
" nt2 = s(\"normal-tangential coordinates\", [ 1.0], 0.0)\n",
" plot([X1[1],X2[1]], [X1[2],X2[2]], \"-ko\")\n",
" X1N1 = X1 + nt1[:,1]*0.5\n",
" X1T1 = X1 + nt1[:,2]*0.5\n",
" plot([X1[1],X1N1[1]], [X1[2],X1N1[2]], \"-r\")\n",
" plot([X1[1],X1T1[1]], [X1[2],X1T1[2]], \"-g\")\n",
" X2N2 = X2 + nt2[:,1]*0.5\n",
" X2T2 = X2 + nt2[:,2]*0.5\n",
" plot([X2[1],X2N2[1]], [X2[2],X2N2[2]], \"-b\")\n",
" plot([X2[1],X2T2[1]], [X2[2],X2T2[2]], \"-y\")\n",
"end\n",
"axis(\"equal\")\n",
"ylim(-0.5, 1.0)\n",
"xlim(-0.5, 4.5)"
]
},
{
"cell_type": "code",
"execution_count": 111,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"i = 1, normal = [-0.19611613513818404,0.9805806756909202], tangent = [0.9805806756909202,0.19611613513818404], dot = 0"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f32fe7874d0>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"(-1.0,5.0,-0.2,1.2000000000000002)"
]
},
"execution_count": 111,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
".0\n",
"i = 2, normal = [0.09142755332923394,0.9958117304451831], tangent = [0.9958117304451831,-0.09142755332923394], dot = 0.0\n",
"i = 3, normal = [-0.11485575612958872,0.9933821798703159], tangent = [0.9933821798703159,0.11485575612958872], dot = 0.0\n",
"i = 4, normal = [-0.15895744828402364,0.9872854347325458], tangent = [0.9872854347325458,0.15895744828402364], dot = 0.0\n",
"i = 5, normal = [0.28734788556634544,0.9578262852211514], tangent = [0.9578262852211514,-0.28734788556634544], dot = 0.0\n"
]
}
],
"source": [
"for s in [s1, s2, s3, s4]\n",
" X1 = s(\"geometry\", [-1.0], 0.0)\n",
" X2 = s(\"geometry\", [ 1.0], 0.0)\n",
" plot([X1[1],X2[1]], [X1[2],X2[2]], \"-ko\")\n",
"end\n",
"for i=1:5\n",
" s = 4*(i-1)+1\n",
" e = s + 1\n",
" normal = vec(P[2*(i-1)+1, s:e])\n",
" s = 4*(i-1)+3\n",
" e = s + 1\n",
" tangent = vec(P[2*(i-1)+2, s:e])\n",
" println(\"i = $i, normal = $normal, tangent = $tangent, dot = \", dot(normal, tangent))\n",
" plot([nodes[i][1], nodes[i][1]+normal[1]*0.5], [nodes[i][2], nodes[i][2]+normal[2]*0.5], \"-r\")\n",
" plot([nodes[i][1], nodes[i][1]+tangent[1]*0.5], [nodes[i][2], nodes[i][2]+tangent[2]*0.5], \"-b\")\n",
"end\n",
"ylim(-0.5, 1.0)\n",
"xlim(-0.5, 4.5)\n",
"axis(\"equal\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.4.2",
"language": "julia",
"name": "julia-0.4"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "0.4.2"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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