Parametric Level-set Based Topology Optimization For Continuous Structures Under Self Weights And Dynamic Topology Optimization

With the improvement of computing capability and the development of structure technology,the architectural structure with the complex appearance and diverse functions has gradually attracted the attention of designers.As a bridge between concept design and structural design,continuous topology optimization generation technology can give consideration to both mechanical performance analysis and architectural structure design.Applying the topological optimization method to the field of architectural design can guarantee good structural performance at the initial stage of design,which is of great practical significance.The main work of this paper is to apply the parameterized level set method based on radial basis function(RBF)to structural topology optimization problems related to architectural design.First of all,this paper uses the parameterized level set method based on RBF as the basic algorithm of topology optimization,introduces the self weights of the structure into the static optimization problem,constructs the optimization model of structural compliant minimization under self weights,and deduces the numerical formulation of the objective function and velocity field.At the same time,compared with the optimization results based on the density method,the influence of the material interpolation function in the density method on the optimization results is explored through theoretical analysis,and the optimization results based on ANSYS are used to prove it.The advantage of the parameterized level set method is proved by numerical examples.Aiming at the same optimization model,by comparing the topology optimization results based on different methods,the inherent correlation is explained,and the necessity of considering self weights in structural design is proved.Secondly,because of the diversity of functions,the building structure is inevitably disturbed by mechanical equipment or other external excitations.the structural design needs to consider its eigenfrequency and keep it away from the frequency range of disturbance excitation as far as possible.to reduce the vibration caused by resonance.Therefore,in this paper,the level set method is applied to solve the eigenfrequency-dependent topology optimization problem.Based on the virtual work principle and boundary evolution method in the classical literature of level set,an optimization model is established,which takes the k-order eigenvalue of the structure as the objective function and the material volume fraction as the constraint condition.Lagrange multiplier is introduced to derive the numerical formula of the velocity field.Numerical examples are given to verify the correctness and effectiveness of the method.The optimized single material combination of solid-blank material is transformed into a doublematerial combination of stiffer and softer materials,and the differences of the final optimized topological shape and objective value under the combination of stiffer materials and different materials are compared.Finally,in view of the non-stationary random excitation such as earthquake,the parameterized level set method is applied to the topology optimization of structural random dynamic response.In this paper,taking the maximum displacement variance of the specified point as the optimization objective and the material volume fraction as the constraint,the optimization model is established.The dynamic response of the structure is solved by the time domain explicit method,and the horizontal set velocity field is derived by the time domain explicit adjoint method.Combined with the horizontal set band method,the flexible topology change is realized,and the continuity and stability of the optimization iterative process are improved.Numerical examples are given to illustrate the law of the optimal topology change of the structure under non-stationary random excitation and to explore the effects of different initial designs on the optimization results in terms of topology form,level set function and optimization objectives.