Abstract
A theorem for planar case and its generalization for spatial case are proposed to determine the projection of a virtual displacement to the orientation under the case of knowing the projections of a virtual displacement to the given two or three orientations for object systems subject to holonomic and scleronomic constraints. Some lemmas corresponding to the two theorems for special cases are given. Applications to structural static analysis are investigated using the two theorems in this paper. Result reveals that the two theorems and corresponding lemmas are easy to be used, shorten the distance between the principle of virtual displacement and its application, and the relating problems can be solved quickly with them.
Highlights
1 Introduction It is well known that the principle of virtual displacement is a main part in analytical statics, and the important basis for analytical dynamics and structural analysis
4 Conclusions This paper mainly faces to the difficulty of computation of virtual work, investigates on the projection of a dot’s virtual displacement to a given orientation, propose two theorems and corresponding lemmas, and discuss their application for analyzing the forces of structural members
Computation procession reveals that the formula for planar situation is easy to use, and the formula for spatial situation is normalized and easy to be remembered
Summary
It is well known that the principle of virtual displacement (or virtual work) is a main part in analytical statics, and the important basis for analytical dynamics and structural analysis. Some current college textbooks [1-7] for engineering mechanics or structural analysis course often propose two main methods for building relations among virtual displacements of different points for the system with holonomic and scleronomic constraints, ie, analytical method and geometrical method.
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