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
Orthotropic materials weakened by a doubly periodic array of cracks under far-field antiplane shear are investigated, where the fundamental cell contains four cracks of unequal size. By applying the mapping technique,...Orthotropic materials weakened by a doubly periodic array of cracks under far-field antiplane shear are investigated, where the fundamental cell contains four cracks of unequal size. By applying the mapping technique, the elliptical function theory and the theory of analytical function boundary value problems, a closed form solution of the whole-field stress is obtained. The exact formulae for the stress intensity factor at the crack tip and the effective antiplane shear modulus of the cracked orthotropic material are derived. A comparison with the finite element method shows the efficiency and accuracy of the present method. Several illustrative examples are provided, and an interesting phenomenon is observed, that is, the stress intensity factor and the dimensionless effective modulus are independent of the material property for a doubly periodic cracked isotropic material, but depend strongly on the material property for the doubly periodic cracked orthotropic material. Such a phenomenon for antiplane problems is similar to that for in-plane problems. The present solution can provide benchmark results for other numerical and approximate methods.展开更多
On the basis of the existing fundamental solutions ofdisplacements, further improvement is made, and then the generalfundamental solutions of both plane elastic and plane plasticproblems for ortho- tropic materials ar...On the basis of the existing fundamental solutions ofdisplacements, further improvement is made, and then the generalfundamental solutions of both plane elastic and plane plasticproblems for ortho- tropic materials are obtained. Two parametersbased on material constants a_1, a_2 are used to derive the rele-vant expressions in a real variable form. Additionally, an analyticalmethod of solving the singular integral for the internal stresses isintroduced, and the corresponding result are given. If a_1=a_2=1, allthe expres- sions obtained for orthotropy can be reduced to thecorresponding ones for isotropy. Because all these expres- sions andresults can be directly used for both isotropic problems andorthotropic problems, it is convenient to use them in engineeringwith the boundary element method (BEM).展开更多
Stress intensity factors （SIFs） for the cracked circular disks under different distributing surface tractions are evaluated with the scaled boundary finite element method （SBFEM）. In the SBFEM, the analytical adva...Stress intensity factors （SIFs） for the cracked circular disks under different distributing surface tractions are evaluated with the scaled boundary finite element method （SBFEM）. In the SBFEM, the analytical advantage of the solution in the radial direction allows SIFs to be directly determined from its definition, therefore no special crack-tip treatment is necessary. Furthermore anisotropic material behavior can be treated easily. Different distributions of surface tractions are considered for the center and double-edge-cracked disks. The benchmark examples are modeled and an excellent agreement between the results in the present study and those in published literature is found. It shows that SBFEM is effective and possesses high accuracy. The SIFs of the cracked orthotropic material circular disks subjected to different surface tractions are also evaluated. The technique of substructure is applied to handle the multiple cracks problem.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.10672008).
文摘Orthotropic materials weakened by a doubly periodic array of cracks under far-field antiplane shear are investigated, where the fundamental cell contains four cracks of unequal size. By applying the mapping technique, the elliptical function theory and the theory of analytical function boundary value problems, a closed form solution of the whole-field stress is obtained. The exact formulae for the stress intensity factor at the crack tip and the effective antiplane shear modulus of the cracked orthotropic material are derived. A comparison with the finite element method shows the efficiency and accuracy of the present method. Several illustrative examples are provided, and an interesting phenomenon is observed, that is, the stress intensity factor and the dimensionless effective modulus are independent of the material property for a doubly periodic cracked isotropic material, but depend strongly on the material property for the doubly periodic cracked orthotropic material. Such a phenomenon for antiplane problems is similar to that for in-plane problems. The present solution can provide benchmark results for other numerical and approximate methods.
文摘On the basis of the existing fundamental solutions ofdisplacements, further improvement is made, and then the generalfundamental solutions of both plane elastic and plane plasticproblems for ortho- tropic materials are obtained. Two parametersbased on material constants a_1, a_2 are used to derive the rele-vant expressions in a real variable form. Additionally, an analyticalmethod of solving the singular integral for the internal stresses isintroduced, and the corresponding result are given. If a_1=a_2=1, allthe expres- sions obtained for orthotropy can be reduced to thecorresponding ones for isotropy. Because all these expres- sions andresults can be directly used for both isotropic problems andorthotropic problems, it is convenient to use them in engineeringwith the boundary element method (BEM).
基金financially supported by the National Natural Youth Foundation of China (Grant Nos. 51109134,51009019, 11102118 and 51208310)the Liaoning Province Education Administration Foundation (Grant No. L2010413)+1 种基金the China Postdoctoral Science Foundation (Grant No. 2011M500557)the Natural Science Foundation of Liaoning Province (Grant No.20102164)
文摘Stress intensity factors （SIFs） for the cracked circular disks under different distributing surface tractions are evaluated with the scaled boundary finite element method （SBFEM）. In the SBFEM, the analytical advantage of the solution in the radial direction allows SIFs to be directly determined from its definition, therefore no special crack-tip treatment is necessary. Furthermore anisotropic material behavior can be treated easily. Different distributions of surface tractions are considered for the center and double-edge-cracked disks. The benchmark examples are modeled and an excellent agreement between the results in the present study and those in published literature is found. It shows that SBFEM is effective and possesses high accuracy. The SIFs of the cracked orthotropic material circular disks subjected to different surface tractions are also evaluated. The technique of substructure is applied to handle the multiple cracks problem.
