The purpose of the present work is to study the buckling problem with plate/shell topology optimization of orthotropic material. A model of buckling topology optimization is established based on the independent, conti...The purpose of the present work is to study the buckling problem with plate/shell topology optimization of orthotropic material. A model of buckling topology optimization is established based on the independent, continuous, and mapping method, which considers structural mass as objective and buckling critical loads as constraints. Firstly, composite exponential function (CEF) and power function (PF) as filter functions are introduced to recognize the element mass, the element stiffness matrix, and the element geometric stiffness matrix. The filter functions of the orthotropic material stiffness are deduced. Then these filter functions are put into buckling topology optimization of a differential equation to analyze the design sensitivity. Furthermore, the buckling constraints are approximately expressed as explicit functions with respect to the design variables based on the first-order Taylor expansion. The objective function is standardized based on the second-order Taylor expansion. Therefore, the optimization model is translated into a quadratic program. Finally, the dual sequence quadratic programming (DSQP) algorithm and the global convergence method of moving asymptotes algorithm with two different filter functions (CEF and PF) are applied to solve the optimal model. Three numerical results show that DSQP&CEF has the best performance in the view of structural mass and discretion.展开更多
Using the plate/shell elements in commercial software,accurate analysis of interlaminar initial damage in typical composite structures is still a challenging issue.To propose an accurate and efficient model for analys...Using the plate/shell elements in commercial software,accurate analysis of interlaminar initial damage in typical composite structures is still a challenging issue.To propose an accurate and efficient model for analysis of interlaminar initial damage,the following work is carried out:(A)A higher-order theory is firstly proposed by introducing the local Legendre polynomials,and then a novel shell element containing initial damage prediction is developed,which can directly predict transverse shear stresses without any postprocessing methods.Unknown variables at each node are independent of number of layers,so the proposed model is more efficient than the 3D-FEM.(B)Compression experiment is carried out to verify the capability of the proposed model.The results obtained from the proposed model are in good agreement with experimental data.(C)Several examples have been analyzed to further assess the capability of the proposed model by comparing to the 3D-FEM results.Moreover,accuracy and efficiency have been evaluated in different damage criterion by comparing with the selected models.The numerical results show that the proposed model can well predict the initial interlaminar damage as well as other damage.Finally,the model is implemented with UEL subroutine,so that the present approach can be readily utilized to analyze the initial damage in typical composite structures.展开更多
The plate-shell structures with stiffeners are widely used in a broad range of engineering structures. This study presents the layout optimization of stiffeners. The minimum weight of stiffeners is taken as the object...The plate-shell structures with stiffeners are widely used in a broad range of engineering structures. This study presents the layout optimization of stiffeners. The minimum weight of stiffeners is taken as the objective function with the global stiffness constraint. In the layout optimization, the stiffeners should be placed at the locations with high strain energy/or stress. Conversely, elements of stiffeners with a small strain energy/or stress are considered to be used inefficiently and can be removed. Thus, to identify the element efficiency so that most inefficiently used elements of stiffeners can be removed, the element sensitivity of the strain energy of stiffeners is introduced, and a search criterion for locations of stiffeners is presented. The layout optimization approach is given for determining which elements of the stiffeners need to be kept or removed. In each iterative design, a high efficiency reanalysis approach is used to reduce the computational effort. The present approach is implemented for the layout optimization of stiffeners for a bunker loaded by the hydrostatic pressure. The numerical results show that the present approach is effective for dealing with layout optimization of stiffeners for plate-shell structures.展开更多
Using the two-scale decomposition technique, the h-adaptive meshless local Petrov- Galerkin method for solving Mindlin plate and shell problems is presented. The scaling functions of B spline wavelet are employed as t...Using the two-scale decomposition technique, the h-adaptive meshless local Petrov- Galerkin method for solving Mindlin plate and shell problems is presented. The scaling functions of B spline wavelet are employed as the basis of the moving least square method to construct the meshless interpolation function. Multi-resolution analysis is used to decompose the field variables into high and low scales and the high scale component can commonly represent the gradient of the solution according to inherent characteristics of wavelets. The high scale component in the present method can directly detect high gradient regions of the field variables. The developed adaptive refinement scheme has been applied to simulate actual examples, and the effectiveness of the present adaptive refinement scheme has been verified.展开更多
An approach is presented for computing the adjoint operator vector of a class of nonlinear （that is, partial-nonlinear） operator matrices by using the properties of conjugate operators to generalize a previous metho...An approach is presented for computing the adjoint operator vector of a class of nonlinear （that is, partial-nonlinear） operator matrices by using the properties of conjugate operators to generalize a previous method proposed by the author. A unified theory is then given to solve a class of nonlinear （partial-nonlinear and including all linear） and non-homogeneous differential equations with a mathematical mechanization method. In other words, a transformation is constructed by homogenization and triangulation, which reduces the original system to a simpler diagonal system. Applications are given to solve some elasticity equations.展开更多
基金supported by the National Natural Science Foundation of China (Grants 11072009, 11172013)the Beijing Education Committee Development Project (Grant SQKM2016100 05001)the Beijing University of Technology Basic Research Fund (Grant 001000514313003)
文摘The purpose of the present work is to study the buckling problem with plate/shell topology optimization of orthotropic material. A model of buckling topology optimization is established based on the independent, continuous, and mapping method, which considers structural mass as objective and buckling critical loads as constraints. Firstly, composite exponential function (CEF) and power function (PF) as filter functions are introduced to recognize the element mass, the element stiffness matrix, and the element geometric stiffness matrix. The filter functions of the orthotropic material stiffness are deduced. Then these filter functions are put into buckling topology optimization of a differential equation to analyze the design sensitivity. Furthermore, the buckling constraints are approximately expressed as explicit functions with respect to the design variables based on the first-order Taylor expansion. The objective function is standardized based on the second-order Taylor expansion. Therefore, the optimization model is translated into a quadratic program. Finally, the dual sequence quadratic programming (DSQP) algorithm and the global convergence method of moving asymptotes algorithm with two different filter functions (CEF and PF) are applied to solve the optimal model. Three numerical results show that DSQP&CEF has the best performance in the view of structural mass and discretion.
基金supported by the National Natural Science Foundation of China(No.12172295)SKLLIM1902the Natural Science Foundation in Shaanxi Province,China(No.2019JQ-909)。
文摘Using the plate/shell elements in commercial software,accurate analysis of interlaminar initial damage in typical composite structures is still a challenging issue.To propose an accurate and efficient model for analysis of interlaminar initial damage,the following work is carried out:(A)A higher-order theory is firstly proposed by introducing the local Legendre polynomials,and then a novel shell element containing initial damage prediction is developed,which can directly predict transverse shear stresses without any postprocessing methods.Unknown variables at each node are independent of number of layers,so the proposed model is more efficient than the 3D-FEM.(B)Compression experiment is carried out to verify the capability of the proposed model.The results obtained from the proposed model are in good agreement with experimental data.(C)Several examples have been analyzed to further assess the capability of the proposed model by comparing to the 3D-FEM results.Moreover,accuracy and efficiency have been evaluated in different damage criterion by comparing with the selected models.The numerical results show that the proposed model can well predict the initial interlaminar damage as well as other damage.Finally,the model is implemented with UEL subroutine,so that the present approach can be readily utilized to analyze the initial damage in typical composite structures.
基金Project supported by the Foundation of University's Doctorial Subjects of China (No.20010183013)985-Automotive Engineering of Jilin University.
文摘The plate-shell structures with stiffeners are widely used in a broad range of engineering structures. This study presents the layout optimization of stiffeners. The minimum weight of stiffeners is taken as the objective function with the global stiffness constraint. In the layout optimization, the stiffeners should be placed at the locations with high strain energy/or stress. Conversely, elements of stiffeners with a small strain energy/or stress are considered to be used inefficiently and can be removed. Thus, to identify the element efficiency so that most inefficiently used elements of stiffeners can be removed, the element sensitivity of the strain energy of stiffeners is introduced, and a search criterion for locations of stiffeners is presented. The layout optimization approach is given for determining which elements of the stiffeners need to be kept or removed. In each iterative design, a high efficiency reanalysis approach is used to reduce the computational effort. The present approach is implemented for the layout optimization of stiffeners for a bunker loaded by the hydrostatic pressure. The numerical results show that the present approach is effective for dealing with layout optimization of stiffeners for plate-shell structures.
基金supported by the Scientific Foundation of National Outstanding Youth of China(No.50225520)Science Foundation of Shandong University of Technology of China(No.2006KJM33).
文摘Using the two-scale decomposition technique, the h-adaptive meshless local Petrov- Galerkin method for solving Mindlin plate and shell problems is presented. The scaling functions of B spline wavelet are employed as the basis of the moving least square method to construct the meshless interpolation function. Multi-resolution analysis is used to decompose the field variables into high and low scales and the high scale component can commonly represent the gradient of the solution according to inherent characteristics of wavelets. The high scale component in the present method can directly detect high gradient regions of the field variables. The developed adaptive refinement scheme has been applied to simulate actual examples, and the effectiveness of the present adaptive refinement scheme has been verified.
基金the National Basic Research Program of China(973Program)(No.2004CB318000)
文摘An approach is presented for computing the adjoint operator vector of a class of nonlinear （that is, partial-nonlinear） operator matrices by using the properties of conjugate operators to generalize a previous method proposed by the author. A unified theory is then given to solve a class of nonlinear （partial-nonlinear and including all linear） and non-homogeneous differential equations with a mathematical mechanization method. In other words, a transformation is constructed by homogenization and triangulation, which reduces the original system to a simpler diagonal system. Applications are given to solve some elasticity equations.
