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The static equilibrium of a mechanical system rigid bodies is defined by the condition that the virtual work of the applied forces is zero for any virtual displacement of the system. This is known as the principle of virtual work. [5] This is equivalent to the requirement that the generalized forces for any virtual displacement are zero, that ...
An example of this is quasi-static expansion of a mixture of hydrogen and oxygen gas, where the volume of the system changes so slowly that the pressure remains uniform throughout the system at each instant of time during the process. [2] Such an idealized process is a succession of physical equilibrium states, characterized by infinite ...
The system oscillates about the equilibrium position under the influence of loads. An iterative process is followed by simulating a pseudo- dynamic process in time, with each iteration based on an update of the geometry, [ 1 ] similar to Leapfrog integration and related to Velocity Verlet integration .
The static equilibrium of a particle is an important concept in statics. A particle is in equilibrium only if the resultant of all forces acting on the particle is equal to zero. In a rectangular coordinate system the equilibrium equations can be represented by three scalar equations, where the sums of forces in all three directions are equal ...
The bending moments and shear forces in Euler–Bernoulli beams can often be determined directly using static balance of forces and moments. However, for certain boundary conditions, the number of reactions can exceed the number of independent equilibrium equations. [5] Such beams are called statically indeterminate.
In computational mechanics, Guyan reduction, [1] also known as static condensation, is a dimensionality reduction method which reduces the number of degrees of freedom by ignoring the inertial terms of the equilibrium equations and expressing the unloaded degrees of freedom in terms of the loaded degrees of freedom.
A body is said to be "free" when it is singled out from other bodies for the purposes of dynamic or static analysis. The object does not have to be "free" in the sense of being unforced, and it may or may not be in a state of equilibrium; rather, it is not fixed in place and is thus "free" to move in response to forces and torques it may experience.
A fundamental result in analytical mechanics is D'Alembert's principle, introduced in 1708 by Jacques Bernoulli to understand static equilibrium, and developed by D'Alembert in 1743 to solve dynamical problems. [21]