In this paper, we use the weak Galerkin （WG） finite element method to solve the mixed form linear elasticity problem. In the mixed form, we get the discrete of proximation of the stress tensor and the displacement f...In this paper, we use the weak Galerkin （WG） finite element method to solve the mixed form linear elasticity problem. In the mixed form, we get the discrete of proximation of the stress tensor and the displacement field. For the WG methods, we define the weak function and the weak differential operator in an optimal polynomial approximation spaces. The optimal error estimates are given and numerical results are presented to demonstrate the efficiency and the accuracy of the weak Galerkin finite element method.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
基金The authors would like to thank China National Natural Science Foundation （91630201, U1530116, 11726102, 11771179）, and the Program for Cheung Kong Scholars of Ministry of Education of China, Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, 3ilin University, Changchun, 130012, P.R. China.
文摘In this paper, we use the weak Galerkin （WG） finite element method to solve the mixed form linear elasticity problem. In the mixed form, we get the discrete of proximation of the stress tensor and the displacement field. For the WG methods, we define the weak function and the weak differential operator in an optimal polynomial approximation spaces. The optimal error estimates are given and numerical results are presented to demonstrate the efficiency and the accuracy of the weak Galerkin finite element method.
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.
