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Abstract The work reported in this thesis is concerned with the economic solution of nonlinear dynamic finite element equations. The nonlinearity is due to the material nonlinearity , the large displacements and rotations or both . The equations are integrated using the methods of direct time integration and mode superposition In direct time integration method the response of the system is dependent on the size of the step t that is dependent on the frequency content of the system. In mode superposition method the response is approximated using only a small number of the lower mode shapes and frequencies which correspond to the initial configuration of the system . This version is denoted by NDYN = 2 Displacements and stresses obtained using NDYN = 2 are revised by adding the effect of the remaining higher modes based on static analysis. There are two an the first, a ~_wo techinques for including this effect, L. first procedure under the static effect is employed, NDYN = 3 , and in the second a linear static effect is |