Structural Optimization Based On Method Of Reduced Degree Of Freedoms

Complex structure is usually discretized by finite element method in order to calculate its mechanics properties and optimize structural parameters. For there are a great deal of DOFs for the discretized stiffness matrix, it is a waste of resources to compute equation of static equilibrium and generalized eigenvalue problems. In this thesis, the displacement condensation method of substructures interfaces and the heterogeneous multi-scale method are used to reduce the DOFs of whole stiffness matrix for the purpose of analyzing and optimizing complex structure.The displacement condensation method of substructures interfaces is widely used in structural dynamical analysis. First, the complex structure is divided into several substructures. Then the stiffness matrix of each sub-structures were condensed into DOFs of each sub-structural interfaces and made into each reduced sub-stiffness matrix. The reduced whole stiffness matrix was assembled by that of each sub-structure. Through a series of condensing and assembling procedure, the whole stiffness matrix was reduced into simple matrix and could be used to calculate the first frequencies. And a systemic program framework made of MATLAB and ANSYS was built to analyze mechanic properties of complex structure by using of the displacement condensation method of substructures interfaces.The heterogeneous multi-scale method, or HMM, is a general framework of designing multi-scale method for a wide variety of application. It is proved to be very useful in guiding the design and analysis of multi-scale methods for many researchers of different disciplines. The heterogeneous multi-scale method with finite element method in each multi-scale, or HMM-FEM, was derived using the philosophy essence of HMM and can be used in linear elastic problems. HMM-FEM was proved to be both simplicity and high efficiency through several numerical examples.