On the basis of the concept of finite element methods, the rigorous analytical solutions of structural response in terms of the design variables are researched in this paper. The spatial trusses are taken as an exampl...On the basis of the concept of finite element methods, the rigorous analytical solutions of structural response in terms of the design variables are researched in this paper. The spatial trusses are taken as an example for the solution of the analytical expressions of the explicit displacements which are proved mathematically; then some conclusions are reached that are useful to structural sensitivity analysis and optimization. In the third part of the paper, a generalized geometric programming method is sugguested for the optimal model with the explicit displacement. Finally, the analytical solutions of the displacements of three trusses are given as examples.展开更多
The temperature fields in the laminated shells were studied, including opencylindrical shells and cylindrical shells, according to the thermal theory. Analyticalsolution of the temperature in the shells with the known...The temperature fields in the laminated shells were studied, including opencylindrical shells and cylindrical shells, according to the thermal theory. Analyticalsolution of the temperature in the shells with the known temperature on the surfaces waspresent. The thinning layer approach was introduced to simplify the three-dimensionalheat conduction equation. Firstly, the layered shell was divided into N thinner layers. Thegoverning equation was simplified by replacing the variable r by r0 in the center line ofevery thin layer. The general solutions of temperature satisfying the simplified threedimensionalgoverning equation in single-layered shell were deduced in the cylindricalcoordinate system. Then, the temperature and heat flux relationships between the surfacescould be found by transferring matrixes. According to the continuities of temperature andheat flux in the interface of the laminates, the temperature and heat flux relationships ofthe surfaces were derived. With the temperature condition on the surfaces, the unknowncoefficients in the general solution of temperature were obtained. Finally, the effects fromthe thinning layer approach were eliminated by analyzing different numbers of thin layers.The validity and accuracy of the proposal method were proved from the convergence andcomparison studies. And several numerical examples were studied to investigated thetemperature effects from surface temperatures, geometric size of the shells andcomposition of layers.展开更多
文摘On the basis of the concept of finite element methods, the rigorous analytical solutions of structural response in terms of the design variables are researched in this paper. The spatial trusses are taken as an example for the solution of the analytical expressions of the explicit displacements which are proved mathematically; then some conclusions are reached that are useful to structural sensitivity analysis and optimization. In the third part of the paper, a generalized geometric programming method is sugguested for the optimal model with the explicit displacement. Finally, the analytical solutions of the displacements of three trusses are given as examples.
基金supported by the Natural ScienceFoundation of Jiangsu Province (Grant No. BK20160519)the Research Foundation forAdvanced Talents of Jiangsu University (Grant No. 16JDG053)+2 种基金the National NaturalScience Foundation of China (Grant No. 51641804)the Natural Science Foundation ofJiangsu Province of China (Grant No. BK20160536)the Advanced Talents ScientificResearch Foundation of Jiangsu University (Grant No. 15JDG170).
文摘The temperature fields in the laminated shells were studied, including opencylindrical shells and cylindrical shells, according to the thermal theory. Analyticalsolution of the temperature in the shells with the known temperature on the surfaces waspresent. The thinning layer approach was introduced to simplify the three-dimensionalheat conduction equation. Firstly, the layered shell was divided into N thinner layers. Thegoverning equation was simplified by replacing the variable r by r0 in the center line ofevery thin layer. The general solutions of temperature satisfying the simplified threedimensionalgoverning equation in single-layered shell were deduced in the cylindricalcoordinate system. Then, the temperature and heat flux relationships between the surfacescould be found by transferring matrixes. According to the continuities of temperature andheat flux in the interface of the laminates, the temperature and heat flux relationships ofthe surfaces were derived. With the temperature condition on the surfaces, the unknowncoefficients in the general solution of temperature were obtained. Finally, the effects fromthe thinning layer approach were eliminated by analyzing different numbers of thin layers.The validity and accuracy of the proposal method were proved from the convergence andcomparison studies. And several numerical examples were studied to investigated thetemperature effects from surface temperatures, geometric size of the shells andcomposition of layers.
