A structural morphogenesis method for frame structure #br#
based on generalized inverse matrix theory
Tu Guigang1,2 Cui Changyu2,3 Wang Jianghong2 Chen Chen1
1. Jilin University, Changchun 130012, China;2. School of Civil engineering, Harbin Institute of Technology, Harbin 150090, China;
3. Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin, 150090, China
Abstract：Generalized inverse matrix theory has been widely applied to the morphological analysis of unstable structures. The shape of unstable structure may change under load until its potential energy reaches the minimum, which corresponds to the equilibrium state of the structure without bending moment. Based on this principle and the generalized inverse matrix theory, a structural morphogenesis method suitable for frame structures is proposed. The bar members in the unstable structure are grouped, and the shape transformation equation governing the shape change of the structure is established under the condition that the total length of the members in each group is unchanged. The generalized inverse matrix theory and potential energy gradient are employed to determine the rapidest descending direction of the potential energy, and the positions of nodes shall be gradually adjusted until the potential energy reaches the minimum. With the introduction of element group and temporary elements, the proposed method can be applied to the morphogenesis of various forms of structures. Reasonable setting of element group and temporary element can realize the reasonable redistribution of element length and internal forces as well as many functions. Based on several numerical examples, the characteristics of the method are explained and its effectiveness is validated.
涂桂刚 崔昌禹 汪江红 陈晨. 基于广义逆矩阵理论的杆系结构形态创构方法#br#[J]. 土木工程学报, 2020, 53(5): 25-31.
Tu Guigang Cui Changyu Wang Jianghong Chen Chen. A structural morphogenesis method for frame structure #br#
based on generalized inverse matrix theory. 土木工程学报, 2020, 53(5): 25-31.
