Fail-safe Topology Optimization Algorithm Of 2-D Truss Structure

The purpose of structure optimization is to design a structure which can achieve certain optimal performance index while it is satisfied with all the boundary conditions. In many cases, the optimized design provides an efficient and economical solution for the application. However, due to the lack of redundancy, such structures may be very vulnerable to a local failure of material. Therefore, local failure of material should be taken into account in the early stage of structural design so that the structures can remain operable in a damaged state. A fail-safe topology optimization algorithm is proposed for truss structures, surrounding which several methods have been deeply discussed.Firstly, the topology optimization of truss structure is considered and Solid Isotropic Microstructures with Penalization(SIMP) is introduced.Secondly, a topology optimization of 2-D structures is proposed. The objective function of the topology optimization is to find out the minimum of strain energy value of the structure and the volume of the structure is set as the constraint conditio n. SIMP is proposed to find the optimal solution. The methodologies for SIMP topology optimization method presented in this paper are programmed using MATLAB.The validity of the methodologies in this paper is proved by several il ustrated examples.Finally, a fail-safe topology optimization algorithm of 2-D truss structure is proposed. The objective function of the optimization is to find out the minimum of strain energy value of structure in the worst case damage configuration. The local failure of material is taken into account by means of adding a min- max formulation to the objective function which aims to minimize the worst case performance. The min- max non differentiable optimization problem is transformed into a differentiable optimization problem. Solid Isotropic Microstructures with Penalization(SIMP) is used to find the optimal solution. The proposed optimization method for fail-safe design is verified by several examples.