SOME APPLICATIONS OF THE MIXED FINITE-ELEMENT METHOD TO THE SOLUTION OF PROBLEMS IN SOLID MECHANICS

摘要

The paper analyzes and considers the application of the mixed finite-element method (FEM) to solve applied problems in solid mechanics. The general theory of mixed projection-mesh algorithms is developed. The reasonableness of the mixed method for elasticity, plasticity, and vibration problems is investigated and is used to formulate the conditions that ensure the stability and convergence of the mixed approximation for displacements, strains, and stresses. A special triangular finite element is set up for two-dimensional and axisymmetric problems. To solve problems of the bending, vibration, and stability of plates, a new hybrid finite element based on the Zienkiewicz triangle is proposed. The mathematical justification of the stability and convergence of the mixed approximation is supplemented with the numerical analysis, which confirms the efficiency of the developed algorithms.