Nonlinear dynamic analysis of quasi-symmetric anisotropic structures

Abstract An efficient computational strategy is presented for the nonlinear dynamic analysis of quasi-symmetric anisotropic structures. A mixed formulation is used with the fundamental unknowns consisting of stress resultants, generalized displacements and velocity components. The governing semi-discrete finite element equations consist of a mixed system of algebraic and ordinary differential equations. The temporal integration of the differential equations is performed by using an explicit half-station central difference method. The three key elements of the strategy are: 1. (a) use of mixed finite element models with independent shape functions for the stress resultants, generalized displacements and velocity components and with the stress resultants allowed to be discontinuous at interelement boundaries 2. (b) operator splitting, or additive decomposition of the different arrays in the governing equations into the contributions to a symmetrized response plus correction terms 3. (c) application of a preconditioned conjugate gradient technique to generate the unsymmetric response of the structure, at each time step, as the sum of symmetric and antisymmetric modes, each obtained using approximately half the degrees of freedom of the original model. The preconditioning matrix is taken to be the matrix associated with the symmetrized response. The effectiveness of the proposed strategy is demonstrated by means of a numerical example and the potential of the proposed strategy for solving more complex nonlinear problems is discussed.