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# جلسه هفدهم: 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

SCRUTINIZATION OF TECHNIQUES TO OPTIMIZING FUNCTIONS OF SEVERAL VARIABLES

### The method of steepest descent

This method is characterized by using the negated value of the first partial derivative or gradient of the descent vector.

### The method of conjugate gradients

The minimization algorithm behaves efficiently in the case of functions of higher order when using conjugate gradient method . This serves as a motive for investigating methods developed for the solution of system of linear equations.

### The method of Newton-Raphson

The basic idea behind this method is to approximate the given function to a quadratic in each iteration and then use the minimum of this quadratic Xt as the starting point for the next iteration.

### The method of Fletcher-Reeves

This method was originally devised by Davidon and later improved by Fletcher and Powell and finally is updated by Reeves. The method avoids explicit construction and inversion of the Hessian matrix k, by using the iterative formula.

The number of methods described  been employed by different researchers to minimize the total potential energy function.

روش بهینه سازی و تعریف ریاضی آن در معادله حرکت دینامیکی

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

پرفسور حشمدار