A new algorithm of structure random response numerical characteristics, named as matrix algebra algorithm of structure analysis is presented.Using the algorithm, structure random response numerical characteristics can easily be got by directly solving linear matrix equations rather than structure motion differential equations.Moreover, in order to solve the corresponding linear matrix equations, the numerical integration fast algorithm is presented.Then according to the results, dynamic design and life-span estimation can be done.Besides, the new algorithm can solve non-proportion damp structure response.
Mei YulinWang XiaomingWang DelunDepartment of Mechanical Engineering,Dalian University of Technology,Dalian 116024,China
Combining the vector level set model, the shape sensitivity analysis theory with the gradient projection technique, a level set method for topology optimization with multi-constraints and multi-materials is presented in this paper. The method implicitly describes structural material interfaces by the vector level set and achieves the optimal shape and topology through the continuous evolution of the material interfaces in the structure. In order to increase computational efficiency for a fast convergence, an appropriate nonlinear speed mapping is established in the tangential space of the active constraints. Meanwhile, in order to overcome the numerical instability of general topology optimization problems, the regularization with the mean curvature flow is utilized to maintain the interface smoothness during the optimization process. The numerical examples demonstrate that the approach possesses a good flexibility in handling topological changes and gives an interface representation in a high fidelity, compared with other methods based on explicit boundary variations in the literature.
