Topology Optimization Design Of Structure Under Multi-variable And Multi-constraint For IFMC

Ideal Functional Material Components (IFMC) is an heterogeneous object, which is designed to achieve the best functional application and constructed by the composite material, the period functional meso-structure (PMS), the functional gradient material (FGM) and/or the homogeneous material, realizing the optimal combination of the material structure with the component performance.At present, most of the study in the field of IFMC optimization is conducted in the optimization with a single constraint However, IFMC needs to satisfy the requirement for coupling various functions, so the study on the optimization of IFMC with multi-variable and multi-constraint has an important meaning.Based on the homogenization theory and combining the finite element method with the optimization theory, this thesis deals with the stiffness optimization of IFMC with multi-variable and multi-constraintThe model of topology optimization for continuum structures with compliance minimization objective, subject to multi-constraint, is proposed. For this topology optimization problem, the finite element method is applied to analyze the equilibrium function and the stress constraint and to get the expression and the iterative format of the constraints. The structure is divided into square finite elements, and the penal ratio of the stress constraint is selected by power-law approach. The improved model is solved by the penalty function method and the optimality criteria methods.A software module is developed on MATLAB platform and this software module has an output of the topology graph, one of the CAE software, ANSYS, is applied to analyzing this topology structure. Through the pre-processing, the process of load and solution and the postprocessing, the stress distribution of different topology structure is found. The stress distribution of the structure with one single constraint and the structure with multi-constraint are compared and analyzed.It can be found that under the same load and boundary conditions, the structure with only one volumetric material density constraint is badly destroyed, while the structure with both thevolumetric material density constraint and the stress constraint is still stable. As a result, the importance of multi-variable and multi-constraint to the optimization of IFMC and the effectiveness of the method applied to these optimization problems are demonstrated.