| Title |
A Study on Static Equilibrium of Constrained Systems |
| Keywords |
constraint ; compatibility condition ; constraint force ; potential energy ; minimization |
| Abstract |
Although Nature basically satisfies the static equilibrium, to give a discrete system geometrical constraints leads to some additional forces to sustain the static equilibrium. This paper presents an explicit static equilibrium equation of elastic structures to satisfy compatibility conditions. Extremizing the difference of total potential energy, which is a quadratic function of the deformation difference of unconstrained and constrained systems, and utilizing the fundamental linear algebra, this study exactly determines the static equilibrium equation including a term to calculate the constraint forces. And it is observed that Nature takes the constraint forces as the minimum values of all forces to satisfy the given geometrical conditions. Through the application of several structures with constraints and its extension to continuous systems, it is shown that the proposed equation is valid. |