added test for zero eigenvalue model (no dirichlet boundaries defined)

src/solvers_modal.jl

@@ -236,26 +236,30 @@ function (solver::Solver{Modal})(; show_info=true, debug=false,
     end
 
     dim = size(K, 1)
-    tic()
 
     nboundary_problems = length(get_boundary_problems(solver))
 
     K_red = K
     M_red = M
+
     if !(P == nothing)
-        info("using custom P")
+        tic()
+        info("Using custom P to make transform K_red = P'*K*P and M_red = P'*M*P")
         K_red = P'*K_red*P
         M_red = P'*M_red*P
-    else
+        t1 = round(toq(), 2)
+        info("Transform ready in $t1 seconds.")
+    elseif nboundary_problems != 0
         info("Eliminate boundary conditions from system.")
         for boundary_problem in get_boundary_problems(solver)
             eliminate_boundary_conditions!(K_red, M_red, boundary_problem, dim)
         end
+        t1 = round(toq(), 2)
+        info("Eliminated boundary conditions in $t1 seconds.")
+    else
+        info("No boundary Dirichlet boundary conditions found for system.")
     end
 
-    t1 = round(toq(), 2)
-    info("Eliminated boundary conditions in $t1 seconds.")
-
     # free up some memory before solution
     if empty_assemblies_before_solution
         for problem in get_field_problems(solver)

test/test_modal_analysis_zero_eigenmodes.jl

@@ -0,0 +1,25 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+using JuliaFEM
+using JuliaFEM.Preprocess
+using JuliaFEM.Postprocess
+using JuliaFEM.Testing
+
+@testset "zero eigenmode model" begin
+    meshfile = Pkg.dir("JuliaFEM") * "/test/testdata/primitives.med"
+    mesh = aster_read_mesh(meshfile, "TETRA_TET10_1")
+    model = Problem(mesh, Elasticity, "TET", 3)
+    update!(model.elements, "youngs modulus", 10.0)
+    update!(model.elements, "poissons ratio", 1.0/3.0)
+    update!(model.elements, "density", 10.0)
+    solver = Solver(Modal)
+    solver.properties.nev = 30
+    push!(solver, model)
+    solver()
+    freqs = solver.properties.eigvals
+    info("freqs: $freqs")
+    freqs_expected = [0.0,0.0,0.0,0.0,0.0,0.0,5.05743,5.05743,7.30374,9.55885,9.55885,18.3471,18.3471,19.124,37.008,37.008,47.25,59.8844,63.0,65.3975,65.3975,88.1879,108.854,108.854,131.702,131.702,221.374,301.326,301.326]
+    @test isapprox(freqs, freqs_expected; atol=1.0e-3)
+end
+