Analysis of Stability and Mechanism of Frames With Partially Rigid Connections

Abstract

A method is presented for stability analysis and finding mechanisms of frames with partially rigid connections. Equilibrium equations are formulated with respect to the reduced vector of member-end forces, for which linear constraints are assigned. The modes of self-equilibrium forces and unstable mechanisms are found using singular value decomposition of the matrix representing equilibrium equations and constraints. An infinitesimal mechanism with small degree of kinematic indeterminacy can be found using limit analysis for an artificial proportional loading condition. The effectiveness of proposed method is demonstrated through examples of frames with rectangular and hexagonal grids.

Second-Order Cone Programming Approach to Design of Linkage Mechanisms With Arbitrarily Inclined Hinges

“…Plastic hinges are replaced with revolute joints that can rotate without external load to generate an infinitesimal mechanism of a linkage [16][17][18]. .…”

“…4(a). Nodes 2 and 4 are supported in yand z-directions, and nodes 3 and 5 are supported in xand z-directions [16][17][18].…”

“…In a manner similar to Ref. [16][17][18], we added eight torsional hinges as indicated with × in Fig. 6 to generate a finite mechanism that has no reaction force in the deformation process.…”

“…In order to extend the methods for planar mechanisms to 3-dimensional mechanisms, it is important to consider a mechanism with partially rigid joints such as revolute and screw joints. Ohsaki et al [16] and Tsuda et al [17] presented a design method of 3-dimensional mechanisms of partially rigid frames based on plastic limit analysis. However, in their method, the hinges are restricted to rotate around specified axes in the orthogonal directions of local coordinates.…”

“…Let h n denote the number of hinges. The conditions for hinge directions are assembled using a which leads to the equilibrium equations of the structure with hinges as[17]…”