| In this dissertation, the analysis and optimization problems of truss structures are studied based on finite element analysis (FEA) and mathematical programming (MP) methods, in aspects of theoretical analysis, algorithms and programming.In the aspect of theoretical analysis: a FEA mathematical model of the truss structure is formulated on the basis of the principle of virtual work. Using the Kuhn-Tucker (K-T) condition of MP, full stress design (FSD) criterion is established for stress constrained optimization problems of truss structures. Applying principle of virtual work, displacement and stress are expressed in a unified form and linearization of constraints, including stress and displacement, is completed. Using it as a base, a quadratic programming (QP) problem is established. Based on Wolfe type Duality Theory and K-T condition, a dual problem of the QP problem is constructed and then converted to a linear complementarity problem (LCP).In the aspect of algorithm: guiding by simplification, solving methods for static and dynamic problems and algorithms for optimization problems are studied. Based on the LDLT decomposition of symmetric matrix and sparsity of stiffness matrix, a variable-band LDLT algorithm is obtained. With a linear transformation, dynamic problem is converted into solving some single variable differential equations.Lemke algorithm is described from a new perspective. A sequential quadratic programming (SQP) algorithm is established for truss optimization. In the aspect of programming: starting from the necessary information to express a matrix, the methods to store a matrix are discussed from a new view and full storage method and one-dimensional variable-band in sparse storage methods are described in details. Using an index-mapping array, bandary conditions and overall stiffness matrix superposition are completed simultaneously. Finally, according to algrithms in this dissertation, programs for FEA and optimization of truss structures are accomplished.
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