Design optimization in the context of finite element modeling (FEM) and analysis (FEA) has been traditionally used to help designers determine optimal structural geometry and/or material property parameters according to objective functions of interest and necessary constraints. In the present paper it is attempted to generalize the design optimization methodology into a program synthesis technique for determining the code necessary to encapsulate the constitutive behavior of the material system required for generalized FEA applications. The core concept behind the methodology followed by our group in the past, has been the experimental identification of a dissipated energy density (DED) function for polymer matrix composites (PMCs) through a non-linear optimization scheme for determining the free coefficients of the sum of the basis functions that are used to construct the DED function and is based on the energy balance of the specimen under testing. The utilized testing generated massive amounts of experimental data that would be produced by exposing PMC specimens to multidimensional loading paths with the help of custom made multi-axial computer-controlled testing machines. The variety of custom environments utilized to implement the analytical and numerical details has often created difficulties in transferring our technology to end users in the design and material communities. The present implementation was greatly enabled by recent advances in finite element techniques and “of the shelf” design optimization integration technologies along with the parallel hardware and software evolution. The program synthesis lies on a process that automatically generates the code of a user material subroutine through minimization of the error between measured and simulated specimen behavior. The generated code can be subsequently used with any geometry and loading specification definable within the limits of the non-linear element library in commercial codes such as ANSYS and ABAQUS.
Three-dimensional finite element stress analysis: The technique and methodology of non-linear property simulation and soft tissue loading behavior for different partial denture designs
