Sui Yun-kang, Guo Tian-fu. The Analytical Solutions Based on the Concept of Finite Element Methods[J]. Applied Mathematics and Mechanics, 1990, 11(4): 301-310.
 Citation: Sui Yun-kang, Guo Tian-fu. The Analytical Solutions Based on the Concept of Finite Element Methods[J]. Applied Mathematics and Mechanics, 1990, 11(4): 301-310.

# The Analytical Solutions Based on the Concept of Finite Element Methods

• Publish Date: 1990-04-15
• 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.
•  [1] Schmit,L.A,and H.Miura,Approximation concepts for efficient structural synthesis.NASA,CR-2556(1976). [2] 钱令希,《工程结构优化设计》,水利电力出版社(1883). [3] 谢邦杰,《线性代数》,人民教育出版社(1978). [4] 隋允康,函数变换下的满应力设计方法。应用力学学报,2 (1987). [5] 隋允康、耿树森,Taylor展式的推广及其在求解数学规划中的应用,工程数学学报,1 (1985). [6] 隋允康、耿树森,广义几何规划二阶缩并的原算法及其在结构优化中的应用,计算结构力学及其应用,1 (1985). [7] 隋允康、由衷.广义几何规划的完全二阶原算法,计算结构力学及其应用,4 (1988).

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