Performance of Walsh-based hybrid-mixed stress analysis

The most relevant aspects involved in the implementation of the stress model of the hybrid-mixed finite element formulation are presented and discussed. In this formulation, the stress and displacement fields in the domain of the element and the displacements on the boundary are simultaneously approximated. Digital Walsh functions are used in all three approximations. Due to the special properties of these functions, it is possible to obtain closed form solutions for the integrals involved in the computation of the structural operators. The governing system is usually very large in dimension, but also well structured and highly sparse. Consequently, the use of adequate algorithms to store and manipulate sparse matrices is essential to ensure the numerical efficiency of the model. The direct and iterative methods most used in the solution of large, sparse systems of linear equations are tested and assessed. Fast transform algorithms are used in the post-processing phase to perform the linear combinations of digital Walsh functions needed to construct the stress and displacement fields from their direct approximations. Linear elastostatic problems are used to illustrate the implementation of the Walsh-based hybrid-mixed stress elements.