Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficul...Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation axe imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate.展开更多
This study provides a comprehensive analysis of collision and impact problems’ numerical solutions, focusing ongeometric, contact, and material nonlinearities, all essential in solving large deformation problems duri...This study provides a comprehensive analysis of collision and impact problems’ numerical solutions, focusing ongeometric, contact, and material nonlinearities, all essential in solving large deformation problems during a collision.The initial discussion revolves around the stress and strain of large deformation during a collision, followedby explanations of the fundamental finite element solution method for addressing such issues. The hourglassmode’s control methods, such as single-point reduced integration and contact-collision algorithms are detailedand implemented within the finite element framework. The paper further investigates the dynamic responseand failure modes of Reinforced Concrete (RC) members under asymmetrical impact using a 3D discrete modelin ABAQUS that treats steel bars and concrete connections as bond slips. The model’s validity was confirmedthrough comparisons with the node-sharing algorithm and system energy relations. Experimental parameterswere varied, including the rigid hammer’s mass and initial velocity, concrete strength, and longitudinal and stirrupreinforcement ratios. Findings indicated that increased hammer mass and velocity escalated RC member damage,while increased reinforcement ratios improved impact resistance. Contrarily, increased concrete strength did notsignificantly reduce lateral displacement when considering strain rate effects. The study also explores materialnonlinearity, examining different materials’ responses to collision-induced forces and stresses, demonstratedthrough an elastic rod impact case study. The paper proposes a damage criterion based on the residual axialload-bearing capacity for assessing damage under the asymmetrical impact, showing a correlation betweendamage degree hammer mass and initial velocity. The results, validated through comparison with theoreticaland analytical solutions, verify the ABAQUS program’s accuracy and reliability in analyzing impact problems,offering valuable insights into collision and impact problems’ nonlinearities and practical strategies for enhancingRC structures’ resilience under dynamic stress.展开更多
In this paper. an analytic method is. presented. for the research of nonlinear Three-dimensional problems of composite laminated plates. The perturbation method and the variational principle are used to satisfy the ba...In this paper. an analytic method is. presented. for the research of nonlinear Three-dimensional problems of composite laminated plates. The perturbation method and the variational principle are used to satisfy the basic differential equations and the boundary conditions of the three-dimensional theory of elasticity. The nonlinear three-dimensional problems are studied .for composite anisotropic circular laminas and laminates subjected to transverse loading. The perturbation series solutions of high accuracy are obtained. A large number of results show that transverse normal stress and transverse shear stresses are very important in the nonlinear three-dimensional analysis of laminated plates.展开更多
Variational principles with nonlinear complementarity and finite-dimensional nonlinear complementarity models for three-dimensional frictional contact problems are established.The existence and uniqueness of the solut...Variational principles with nonlinear complementarity and finite-dimensional nonlinear complementarity models for three-dimensional frictional contact problems are established.The existence and uniqueness of the solutions to the finite-dimensional models are proved.A minimum principle is developed and a minimization algorithm is presented.Numerical calculation shows that the algorithm is highly efficient,reliable and promising.展开更多
According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrica...According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically, which can fully characterize the initial-boundary-value problem of this kind of dynamics. An ifnportant integral relation is made, which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechanics. Based on such relationship, it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures, but also to derive systematically the complementary functionals for five-field, four-field, three-field and two-field unconventional Hamilton-type variational principles, and the functional for the unconventional Hamilton-type variational principle in phase space and the potential energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the generalized Legendre transformation given in this paper, Furthermore, the intrinsic relationship among various principles can be explained clearly with this approach.展开更多
基金Project supported by the National 973 Program (No.2004CB719402), the National Natural Science Foundation of China (No. 10372030)the Open Research Projects supported by the Project Fund of the Hubei Province Key Lab of Mechanical Transmission & Manufacturing Engineering Wuhan University of Science & Technology (No.2003A16).
文摘Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation axe imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate.
基金the authority of the National Natural Science Foundation of China(Grant Nos.52178168 and 51378427)for financing this research work and several ongoing research projects related to structural impact performance.
文摘This study provides a comprehensive analysis of collision and impact problems’ numerical solutions, focusing ongeometric, contact, and material nonlinearities, all essential in solving large deformation problems during a collision.The initial discussion revolves around the stress and strain of large deformation during a collision, followedby explanations of the fundamental finite element solution method for addressing such issues. The hourglassmode’s control methods, such as single-point reduced integration and contact-collision algorithms are detailedand implemented within the finite element framework. The paper further investigates the dynamic responseand failure modes of Reinforced Concrete (RC) members under asymmetrical impact using a 3D discrete modelin ABAQUS that treats steel bars and concrete connections as bond slips. The model’s validity was confirmedthrough comparisons with the node-sharing algorithm and system energy relations. Experimental parameterswere varied, including the rigid hammer’s mass and initial velocity, concrete strength, and longitudinal and stirrupreinforcement ratios. Findings indicated that increased hammer mass and velocity escalated RC member damage,while increased reinforcement ratios improved impact resistance. Contrarily, increased concrete strength did notsignificantly reduce lateral displacement when considering strain rate effects. The study also explores materialnonlinearity, examining different materials’ responses to collision-induced forces and stresses, demonstratedthrough an elastic rod impact case study. The paper proposes a damage criterion based on the residual axialload-bearing capacity for assessing damage under the asymmetrical impact, showing a correlation betweendamage degree hammer mass and initial velocity. The results, validated through comparison with theoreticaland analytical solutions, verify the ABAQUS program’s accuracy and reliability in analyzing impact problems,offering valuable insights into collision and impact problems’ nonlinearities and practical strategies for enhancingRC structures’ resilience under dynamic stress.
文摘In this paper. an analytic method is. presented. for the research of nonlinear Three-dimensional problems of composite laminated plates. The perturbation method and the variational principle are used to satisfy the basic differential equations and the boundary conditions of the three-dimensional theory of elasticity. The nonlinear three-dimensional problems are studied .for composite anisotropic circular laminas and laminates subjected to transverse loading. The perturbation series solutions of high accuracy are obtained. A large number of results show that transverse normal stress and transverse shear stresses are very important in the nonlinear three-dimensional analysis of laminated plates.
基金Project supported by the National Natural Science Foundation of China.
文摘Variational principles with nonlinear complementarity and finite-dimensional nonlinear complementarity models for three-dimensional frictional contact problems are established.The existence and uniqueness of the solutions to the finite-dimensional models are proved.A minimum principle is developed and a minimization algorithm is presented.Numerical calculation shows that the algorithm is highly efficient,reliable and promising.
基金Project supported by the National Natural Science Foundation of China(No.10172097)the Doctoral Foundation of Ministry of Education of China(No.20030558025)
文摘According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically, which can fully characterize the initial-boundary-value problem of this kind of dynamics. An ifnportant integral relation is made, which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechanics. Based on such relationship, it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures, but also to derive systematically the complementary functionals for five-field, four-field, three-field and two-field unconventional Hamilton-type variational principles, and the functional for the unconventional Hamilton-type variational principle in phase space and the potential energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the generalized Legendre transformation given in this paper, Furthermore, the intrinsic relationship among various principles can be explained clearly with this approach.
