一类指定应力问题的变分原理与应用

Abstract

To solve some problems in the finite element analysis with specified conditions for stresses or internal forces, the inelastic strain as an additional unknown to meet the specified stress condition was introduced. The elastic mechanics governing equations meeting the specified stress conditions were described under the small deformation assumption. The potential variational principle and the virtual work equation were established with the displacements and unknown inelastic strains as independent variables. Then a generalized variational principle with 4 types of independent variables of the displacement, the elastic strain, the unknown inelastic strain and the stress, was presented. Based on the variational principle, the specified axial forces and the required adjustment quantities were arranged in a dual form in the equations for truss and beam elements. The ordinary stress analysis was realized under the condition with known adjustment quantities, and the required adjustment quantities were obtained with specified axial force conditions. The effects of material stiffness and internal force of a structure were considered in the new method with the prestressing reinforcement simulation improved based on the equivalent load method or the real physical reinforcement method. The method applies to the optimization and adjustment of cable forces in related structures. Numerical simulations of displacement optimization and cable tension adjustment for a cablestayed structure demonstrate the feasibility and accuracy of the presented theory and algorithm.