On the Solution of Elliptic Equation (sum from k-0 to n) akΔkφ=0 and Its Application in Mechanics

Applied Mathematics and Mechanics (English Edition) ›› 1981, Vol. 2 ›› Issue (4): 487-498.

On the Solution of Elliptic Equation (sum from k-0 to n) a_kΔ^kφ=0 and Its Application in Mechanics

盖秉政

Haerbin Institute of Technology, Haerbin

收稿日期:1980-03-11 出版日期:1981-07-18 发布日期:1981-07-18

On the Solution of Elliptic Equation (sum from k-0 to n) a_kΔ^kφ=0 and Its Application in Mechanics

Gai Bing-zheng

Haerbin Institute of Technology, Haerbin

Received:1980-03-11 Online:1981-07-18 Published:1981-07-18

摘要/Abstract

摘要： In this paper, the solution of elliptic equation (sum from k-0 to n) a_kΔ^kφ=0 is discussedin detail by the method of separation of variables in complex field. The general solution which can be used in the approximation to the boundary conditions of the practical problems is presented. Two practical examples in mechanics are given.

关键词: discrete variables, structure optimization, topological optimization, dynamic stress constraint, dynamic displacement constraint

Abstract: In this paper, the solution of elliptic equation (sum from k-0 to n) a_kΔ^kφ=0 is discussedin detail by the method of separation of variables in complex field. The general solution which can be used in the approximation to the boundary conditions of the practical problems is presented. Two practical examples in mechanics are given.

Key words: discrete variables, structure optimization, topological optimization, dynamic stress constraint, dynamic displacement constraint

盖秉政. On the Solution of Elliptic Equation (sum from k-0 to n) a_kΔ^kφ=0 and Its Application in Mechanics[J]. Applied Mathematics and Mechanics (English Edition), 1981, 2(4): 487-498.

Gai Bing-zheng. On the Solution of Elliptic Equation (sum from k-0 to n) a_kΔ^kφ=0 and Its Application in Mechanics[J]. Applied Mathematics and Mechanics (English Edition), 1981, 2(4): 487-498.

[1]	石连栓;孙焕纯;冯恩民. A METHOD FOR TOPOLOGICAL OPTIMIZATION OF STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS AND DISPLACEMENT CONSTRAINTS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(7): 781-787.
[2]	柴山;孙焕纯. A COMBINAT0RIAL ALGORITHM FOR THE DISCRETE OPTIMIZATION OF STRUCTURES[J]. Applied Mathematics and Mechanics (English Edition), 1997, 18(9): 847-856.

On the Solution of Elliptic Equation (sum from k-0 to n) a_kΔ^kφ=0 and Its Application in Mechanics

On the Solution of Elliptic Equation (sum from k-0 to n) a_kΔ^kφ=0 and Its Application in Mechanics

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