scholarly journals Learning The Virtual Work Method In Statics: What Is A Compatible Virtual Displacement?

2020 ◽  
Author(s):  
Ing-Chang Jong
Keyword(s):  
Virtual Work ◽  
Virtual Displacement ◽  
Work Method

Velocity, Acceleration, and Static-Force Analyses of Spatial Linkages

1965 ◽  
Vol 32 (4) ◽  
pp. 903-910 ◽  
Author(s):  
J. Denavit ◽  
R. S. Hartenberg ◽  
R. Razi ◽  
J. J. Uicker
Keyword(s):  
Virtual Work ◽  
Algebraic Method ◽  
Degree Of Freedom ◽  
Static Force ◽  
Virtual Displacement ◽  
Single Loop ◽  
Loop Equation ◽  
The Matrix ◽  
Spatial Linkages

The algebraic method using 4 × 4 matrices is extended to the analysis of velocities, accelerations, and static forces in one-degree-of-freedom, single-loop, spatial linkages consisting of revolute and prismatic pairs, either singly or in combination. The methods are well suited for machine calculations and have been tested on a number of examples, one of which is presented. Velocities and accelerations are obtained by differentiation of the matrix-loop or position equation. Static forces are found by combining the method of virtual work with the matrix-loop equation to relate the virtual displacement of the load to given virtual deformations of the links.

scholarly journals Generalized Lagrange-D’Alembert principle

2012 ◽  
Vol 91 (105) ◽  
pp. 49-58
Author(s):  
Djordje Djukic
Keyword(s):  
Dynamic Equilibrium ◽  
Virtual Work ◽  
Analytical Mechanics ◽  
Principle Of Virtual Work ◽  
Constraint Forces ◽  
Lagrange Equations ◽  
Virtual Displacement ◽  
Generalized Coordinates ◽  
D’Alembert Principle ◽  
Applied Forces

The major issues in the analysis of the motion of a constrained dynamic system are to determine this motion and calculate constraint forces. In the analytical mechanics, only the first of the two problems is analyzed. Here, the problem is solved simultaneously using: 1) Principle of liberation of constraints; 2) Principle of generalized virtual displacement; 3) Idea of ideal constraints; 4) Concept of generalized and ?supplementary" generalized coordinates. The Lagrange-D?Alembert principle of virtual work is generalized introducing virtual displacement as vectorial sum of the classical virtual displacement and virtual displacement in the ?supplementary" directions. From such principle of virtual work we derived Lagrange equations of the second kind and equations of dynamical equilibrium in the ?supplementary" directions. Constrained forces are calculated from the equations of dynamic equilibrium. At the same time, this principle can be used for consideration of equilibrium of system of material particles. This principle simultaneously gives the connection between applied forces at equilibrium state and the constrained forces. Finally, the principle is applied to a few particular problems.

Plastic design of regular orthotropic grids with two adjacent edges fixed, free, or hinged

1972 ◽  
Vol 7 (4) ◽  
pp. 279-284 ◽  
Author(s):  
M Grigorian
Keyword(s):  
Lower Bound ◽  
Virtual Work ◽  
The Other ◽  
Plastic Design ◽  
Simply Supported ◽  
Torsional Resistance ◽  
Plastic Analysis ◽  
Cantilevered Beams ◽  
Flat Grids ◽  
Work Method

Lower-bound solutions to the problem of collapse of regular rectangular, orthotropic grids with two adjacent edges clamped and the other two either free or simply supported and carrying a uniform concentration of normal nodal forces are developed. The virtual-work method of plastic analysis is used to derive generalized formulae for grids composed of cantilevered and propped-cantilevered beams. The uniqueness of the work-method solutions are confirmed by use of the techniques of discrete field mechanics. The present study is restricted to flat grids with uniform members possessing no torsional resistance. An example is provided to illustrate the applications of the proposed solutions.

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