A Reduced Basis Approach for Rapid and Reliable Computation of Structural Linear Elasticity Problems Using Mixed Interpolation of Tensorial Components Element

As the reduced basis method is well used in some other fields to rapidly solve engineer systems, it is adapted to structural computation here. In this article, a reduced basis approach of computing structural linear elasticity problems is proposed to obtain rapid and reliable outputs using mixed interpolation of tensorial components elements. The procedure is as follows. First, structural computation problems based on finite element formulation should be parameterized. As an example, finite element formulation based on a type of element is analyzed and parameters in the formulation are extracted explicitly. Parameterized structural problem is built by assembling finite element formulation of components with parameters. Then, an approximate subspace of lower dimension based on structural outputs within whole parameter domain is constructed by an adaptive procedure. By projecting the parameterized structural problem onto that subspace, it is reduced to a parameterized lower dimension problem, which can be solved rapidly with random given parameters. The procedure is divided into two phases, naming offline and online procedure. Structures in vehicle design problems are employed to verify the feasibility of the procedure and deviation of the accuracy. The results showed that reduced basis approach of structural computation is applicable and efficient.