| In recent years, with the development of technology and the increasing needs of people's live, people encounter more and more complicated multi-field coupling problems in many fields, such as the aerospace field, manufacturing parts of micro-electromechanical systems and transportation. With rapid development of computer technology, modeling and numerical solution strategies, people have already made some achievements and progress in coupling fields. However, there is rarely a unified analysis and optimization approach that can handle most problems. Currently, only specific issues have solutions. What's more, these methods have very high requirements for the users, which cause much inconvenience for application.This thesis describes the phenomenon of multi-field coupling problems. According to different characteristics of multi-field coupling problems, classifications are made and the current commonly used methods and software to solve multi-field coupling problems are summarized. In specific, a summary of the formulation and solutions of structural analysis problem of piezoelectric trusses is presented. The condensation and direct LU decomposition methods are investigated in details, which are for the solution of the system equations with non-symmetric coefficient matrix. Moreover, characteristics of these two methods are summarized. Finally, with the consideration of the relative advantages of direct LU decomposition method, a new algorithm based on the LU decomposition method is proposed for the analysis and optimization of the piezoelectric truss structure. In addition, optimizations are conducted to control strength of piezoelectric truss in this paper. The applied voltage can improve the work of state structures and structural capacity.In this paper, all algorithms are implemented in FORTRAN language and there are no experiments involved in. And the corresponding findings of this paper are verified through numerical examples and comparisons with results in the literature.
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