Topology optimization of continuum structures with design-dependent loads has long been a challenge. In this paper, the topology optimization of 3D structures subjected to design-dependent loads is investigated. A bou...Topology optimization of continuum structures with design-dependent loads has long been a challenge. In this paper, the topology optimization of 3D structures subjected to design-dependent loads is investigated. A boundary search scheme is proposed for 3D problems, by means of which the load surface can be identified effectively and efficiently, and the difficulties arising in other approaches can be overcome. The load surfaces are made up of the boundaries of finite elements and the loads can be directly applied to corresponding element nodes, which leads to great convenience in the application of this method. Finally, the effectiveness and efficiency of the proposed method is validated by several numerical examples.展开更多
For the topology optimization of structures with design-dependent pressure,an intuitive way is to directly describe the loading boundary of the structure,and then update the load on it.However,boundary recognition is ...For the topology optimization of structures with design-dependent pressure,an intuitive way is to directly describe the loading boundary of the structure,and then update the load on it.However,boundary recognition is usually cumbersome and inaccurate.Furthermore,the pressure is always loaded either outside or inside the structure,instead of both.Hence,the inner enclosed and outer open spaces should be distinguished to recognize the loading surfaces.To handle the above issues,a thermal-solid–fluid method for topology optimization with design-dependent pressure load is proposed in this paper.In this method,the specific void phase is defined to be an incompressible hydrostatic fluid,through which the pressure load can be transferred without any needs for special loading surface recognition.The nonlinear-virtual thermal method(N-VTM)is used to distinguish the enclosed and open voids by the temperature difference between the enclosed(with higher temperature)and open(with lower temperature)voids,where the solid areas are treated as the thermal insulation material,and other areas are filled with the self-heating highly thermally conductive material.The mixed displacement–pressure formulation is used to model this solid–fluid problem.The method is easily implemented in the standard density approach and its effectiveness is verified and illustrated by several typical examples at the end of the paper.展开更多
Extensibility and attainability of topology optimization are discussed by investigating a variety of simultaneous topology opti-mization methods extended from the standard formulation.First,the state of the art is hig...Extensibility and attainability of topology optimization are discussed by investigating a variety of simultaneous topology opti-mization methods extended from the standard formulation.First,the state of the art is highlighted through systematic classification of developed methods,such as simultaneous topology optimizations of microstructure and macrostructure,structure and supports,structure and design-dependent loads,structure and locations of involved components.Second,some recent results about simultaneous topology optimization of structure and applied loads are presented.It is shown that the simultaneous topology optimization is an integrated methodology that extends the concept of standard topology optimization in the sense of systematic design.The presence of more than one kind of design variable of different nature makes the optimization problem complex but enlarges the design space to attain the optimization.展开更多
基金supported by the National Natural Science Foundation of China(90816025,10721062)National Basic Research Program of China(2006CB601205)Program for New Century Excellent Talents in University of the Ministry of Education of China(NCET-04-0272)
文摘Topology optimization of continuum structures with design-dependent loads has long been a challenge. In this paper, the topology optimization of 3D structures subjected to design-dependent loads is investigated. A boundary search scheme is proposed for 3D problems, by means of which the load surface can be identified effectively and efficiently, and the difficulties arising in other approaches can be overcome. The load surfaces are made up of the boundaries of finite elements and the loads can be directly applied to corresponding element nodes, which leads to great convenience in the application of this method. Finally, the effectiveness and efficiency of the proposed method is validated by several numerical examples.
基金support to this work by the National Natural Science Foundation of China (Grant Nos.U1808215 and 11821202)the 111 Project (B14013)the Fundamental Research Funds for the Central Universities of China (DUT21GF101).
文摘For the topology optimization of structures with design-dependent pressure,an intuitive way is to directly describe the loading boundary of the structure,and then update the load on it.However,boundary recognition is usually cumbersome and inaccurate.Furthermore,the pressure is always loaded either outside or inside the structure,instead of both.Hence,the inner enclosed and outer open spaces should be distinguished to recognize the loading surfaces.To handle the above issues,a thermal-solid–fluid method for topology optimization with design-dependent pressure load is proposed in this paper.In this method,the specific void phase is defined to be an incompressible hydrostatic fluid,through which the pressure load can be transferred without any needs for special loading surface recognition.The nonlinear-virtual thermal method(N-VTM)is used to distinguish the enclosed and open voids by the temperature difference between the enclosed(with higher temperature)and open(with lower temperature)voids,where the solid areas are treated as the thermal insulation material,and other areas are filled with the self-heating highly thermally conductive material.The mixed displacement–pressure formulation is used to model this solid–fluid problem.The method is easily implemented in the standard density approach and its effectiveness is verified and illustrated by several typical examples at the end of the paper.
基金supported by the National Natural Science Foundation of China(Grant Nos.51275424,51221001)the National Basic Research Program of China("973"Project)(Grant No.2011CB610304)+1 种基金the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20126102130003)the NWPU Foundation for Fundamental Research(Grant No.NPU-FFR-201001)
文摘Extensibility and attainability of topology optimization are discussed by investigating a variety of simultaneous topology opti-mization methods extended from the standard formulation.First,the state of the art is highlighted through systematic classification of developed methods,such as simultaneous topology optimizations of microstructure and macrostructure,structure and supports,structure and design-dependent loads,structure and locations of involved components.Second,some recent results about simultaneous topology optimization of structure and applied loads are presented.It is shown that the simultaneous topology optimization is an integrated methodology that extends the concept of standard topology optimization in the sense of systematic design.The presence of more than one kind of design variable of different nature makes the optimization problem complex but enlarges the design space to attain the optimization.
