Research On Continuum Structural Topological Optimization Technique With Condensation Of Stress Constraints

Structural topological optimization with stress constraints is one of the most difficult and promising subjects in topology optimization design. Compared with some literature on topological optimization with compliance constraints,there are less published papers on stress constraints.There still exist some problems in topology optimization based on stress constraints, such as stress singularity, stress concentrations and approximate equivalent optimization model. Therefore, the research on the topological optimization problem with stress constraints is of significant theory and engineering application value.In order to resolve the minimum volume problems with stress constraints, a large number of numerical simulations are given and the variation features of stress field and related condensation functions based on some existing methods are analyzed in this theses. Continuum structural topological optimization technology based on stress gradient and condensation of stress constraints are proposed, corresponding algorithms are established and several examples for the verification of the proposed technique are given in this theses.The RAMP filtering function and an effective qp approach are adopted to resolve stress singularity phenomenon. A discrete condition of density variables and a q1-norm measure function of global stress are used as penalty functions of the objective function in a given simple optimization model, and several most potential active stress constraints and a KS overall condensation function of stress constraints are used as stress constraints, which reduces computing scale and controls local stress. A MMA approximation method is adopted to obtain an approximate quadratic explicit function for the q1-norm measure stress function of the structure. Combining with a varying stress limit scheme, a more efficiency algorithm for the optimization problem is built. Numerical simulations show the feasibility and the advantages and disadvantages of the method.Then, stress gradient approximation measure is defined and introduced. Several most potential active stress constraints and a overall condensation function of stress gradient replaces stress constraints, a new minimum volume topology optimization equivalent model with stress constraints is constructed. A quadratic programming algorithm is to solve the model, which incorporated with the MMA approximated expansions of these several constraint functions, and numerical simulations are completed.However, one or several condensation functions of stress constraints used as penalty terms of object function is empirical and not reasonable for the optimization problem with stress constraints. The equivalence of the reduced optimization model with the original optimization problem model and engineering applicability of the reduced optimization model still need to be made a research. To solve stress concentration problem and overcome some key technical problems, such as an approximate equivalent reduced optimization model, a set of optimal model reduction and solving technology is proposed in this theses. Firstly, several approximate normal distribution functions are introduced as weight functions of several q-norm functions of structural stresses, which constructs several weighted overall condensation functions of stress constraints. Secondly, the overall condensation constraint function of stress gradient is also introduced. An approximate reduction optimization model with good equivalence is built, by use of a varied stress limit scheme and a trust-region of design variables, all these condensation constraint functions, which can solve the stress concentration problem and control local stresses. Thirdly, an approximate smoothing function of the closed solutions in a transferring dual sub-problem, and a new dual solving algorithm is proposed. Finally, a set of continuum structural topological optimization technology are established, based on stress gradient and condensation of stress constraints and corresponding algorithm. Simultaneously,several verification examples are given.The results of example simulations show that the proposed method based on stress gradient and condensation of stress constraints can resolve topological optimization problems with stress constraints, and get better black/white distribution. It verifies that the reliability and efficiency of the proposed method, and the proposed method is of good theoretical and engineering application value.