الفهرس 
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Abstract
This work is concerned with the development of efficient and accurate method for failure
analysis of steel structures where the developed method can follow structural behavior
from zero loading, failure initiation and propagation till the global failure occurrence with
very high accuracy.
To address the efficient failure analysis of structures, a new numerical analysis method,
namely FEM-β, has been developed in its elastic version. The key characteristic of FEM-β
is the particle discretization that uses two sets of conjugate geometries to discretize the
displacement and stress functions. FEM-β provides block-spring modeling with
equivalence to continuum. It solves accurately the boundary value problem like the
ordinary Finite Element method (FEM). Besides, it describes efficiently the failure
behavior like Distinct Element Method (DEM). Moreover, it has the option to introduce
local imperfection to the model.
In this thesis, FEM-β is newly extended to carry out the nonlinear analysis of steel
structures to achieve more realistic results for failure problems. As FEM-β assures the
equivalence to continuum, it is somehow difficult to include the nonlinear analysis. A
program, coded in C language, has been developed. The program has high applicability
and efficiency where it employs different analysis types, four algorithms for solution of
nonlinear equations, five convergence criteria, the most two popular yield criteria for steel
material and the most accurate return mapping algorithm for stress updating. These options
give our program the applicability to various types of problems. The program has been
verified by comparing the results with the analytical solutions and other existing software
programs. The extended nonlinear method showed high accuracy and it can easily achieve
the failure load. It has the same accuracy of ordinary FEM with triangular elements. This
high accuracy cannot be obtained by discrete elements methods like DEM. A study for the
effect of the imperfection on the nonlinear solution of the extended method has been
conducted.