Application of meta-modeling based finite element solution conversion method to develop smart initial guess of conjugate gradient method for solid element simulation

Abstract

Smart initial guess of Conjugate Gradient (CG) method for solid finite element simulation is developed by using the meta-modeling based finite element solution conversion method. The key feature of this solution conversion method is the rigorousness; the meta-modeling ensures that the most appropriate structural or solid element solution is the one that is close to the solid or structural element solution, respectively, since an error between structural and solid element solutions is accurately defined in a solution space of continuum mechanics. The initial guess of CG method of this study is developed by using an approximate solid element solution which is converted from a relevant structural element solution. Two numerical examples; a cantilever beam and frame problems, of the proposed CG method are presented. The results show that the computational cost is significantly reduced in the proposed CG method as compared to the ordinary CG method. There is an expectation that this reduction of computational cost of solid element simulation will become more significant with the size of the problem targeted.