A finite element mesh optimization procedure using a thermal expansion analogy

Finite element optimum meshes are synthesized by the use of thermal expansion principles in conjunction with an analogous temperature field computed from the element strain energy contents. Elements having high strain energy contents are shrunk and those with low strain energy contents are expanded until all elements contain the same amount of strain energy. Deviatoric strain energy is also used in place of the strain energy as the objective function for the optimization method. Both objective functions yield significant improvements of the meshes after only a few iterations. In one test case, the errors in the maximum stresses are reduced by more than 1/3 after 1 iteration. In another test case, the error in the stress concentration factor is reduced by more than 3/4 after 7 iterations.