Computational Strategy for Analysis of Quasi-Symmetric Structures

An efficient computational strategy is presented for reducing the cost of generating the response of quasi-symmetric structures. The three key elements of the strategy are: a) Use of mixed finite element models having independent shape functions for the internal forces (stress resultants) and generalized displacements with the internal forces allowed to be discontinuous at interelement boundaries; b) operator splitting, or additive decomposition of the different arrays in the governing equations into the contributions to a symmetrized response plus correction terms; and c) application of a preconditioned conjugate gradient technique to generate the unsymmetric response 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 two numerical examples of an anisotropic shallow panel with a quadrilateral plan-form, and an anistropic conical panel. Also, the potential of the proposed strategy for solving nonlinear problems of quasi-symmetric structures is discussed.

[1]  Ahmed K. Noor,et al.  Recent advances in reduction methods for instability analysis of structures , 1983 .

[2]  Ahmed K. Noor,et al.  On making large nonlinear problems small , 1982 .

[3]  A. Noor,et al.  Model‐size reduction for the analysis of symmetric structures with asymmetric boundary conditions , 1987 .

[4]  Ahmed K. Noor,et al.  EXPLOITING SYMMETRIES FOR EFFICIENT POST-BUCKLING ANALYSIS OF COMPOSITE PLATES , 1976 .

[5]  Ahmed K. Noor,et al.  Preconditioned conjugate gradient technique for the analysis of symmetric anisotropic structures , 1987 .

[6]  A. K. Noor,et al.  Nonlinear analysis of anisotropic panels , 1986 .

[7]  Bernard Budiansky,et al.  Notes on nonlinear shell theory. , 1968 .

[8]  J. L. Sanders,et al.  NONLINEAR THEORIES FOR THIN SHELLS , 1963 .

[9]  Ahmed K. Noor,et al.  Model-size reduction technique for the analysis of symmetric anisotropic structures , 1985 .

[10]  Ahmed K. Noor,et al.  Exploiting symmetries for efficient post-buckling analysis of composite plates , 1977 .

[11]  Loyce M. Adams,et al.  An M-Step preconditioned Conjugate Gradient Method for Parallel Computation , 1983, ICPP.

[12]  Ahmed K. Noor,et al.  Symmetry considerations for anisotropic shells , 1976 .

[13]  D. Kershaw.  The incomplete Cholesky—conjugate gradient method for the iterative solution of systems of linear equations , 1978 .

[14]  Ahmed K. Noor,et al.  Mixed models and reduced/selective integration displacement models for nonlinear shell analysis , 1982 .