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# جلسه نهم: آموزش جامع روش های پیشرفته آنالیز دینامیکی غیر خطی (دکتر حشمدار)

AN EFFICIENT METHOD FOR NONLINEAR DYNAMIC ANALYSIS OF 3D SPACE STRUCTURES

Prof.Dr.Hashamdar

## The equation of motion and their solution

The dynamic problems don’t have a single solution like static counterparts. Instead the analyst must establish a succession of solution corresponding to all times of interest in the response period. In the dynamic problems the task of the analyst is to solve the differential equations arising from the equilibrium of the dynamic forces acting on the mass. The differential equation of motion themselves could be derived using Hamilton’s principle, the principle of virtual displacements or direct equilibration of the dynamic forces uses D’Alembert’s principle  .

### Hamilton’s principle

Hamilton’s principle demonstrates that the dynamics of a physical system is recognized by a variation problem for a functional corresponding a single function. The variation problem is equivalent to permit for the derivation of the various equations of motion of the physical system. Hamilton’s principle explains that the true evolution of a system described by generalized coordinates between two specified times. The simple example of such a problem is to achieve the curve of small length connecting two points.

معادله حرکت و روشهای حل آن

آموزش جامع روش های پیشرفته آنالیز دینامیکی غیر خطی سازه های فضائی سه بعدی

پرفسور حشمدار 