AN EFFICIENT METHOD FOR NONLINEAR DYNAMIC ANALYSIS OF 3D SPACE STRUCTURES
In the dynamic problem, the task of the analyst is to solve the differential equation arising from the equilibrium of the dynamic forces on the mass. Equilibrium of dynamic forces is established at the beginning and end of each time interval. For this reason, the devising of a proposed method which considers the establishment of each time interval for dynamic analysis under linear and nonlinear structural behaviour is necessary.
Hence, the proposed method should be applicable for the dynamic response analysis of the linear analysis and it should be possible to extend its application to the nonlinear analysis. The new sets of eigenvectors and eigenvalues for each time step for the proposed theory should not be required and stability and accuracy should be achieved. It is anticipated that the proposed theory could be used to evaluate the dynamic response analysis of nonlinear systems based on the response for a series of short time intervals.
The proposed theory should be able to converge more rapidly to the neighbourhood of the solution and achieve good accuracy cause of less iteration to achieve result. It is anticipated that that the proposed theory could be used as a new technique for minimization of total potential energy function, especially in cases where the number of variables is large. The proposed method is based on the step-by-step time integration of the equations of motion. The majority of these methods have been used to minimize the function representing the total potential energy of 3D space structures subjected to static load. The proposed theory converges more rapidly to the neighbourhood of the solution and achieves good accuracy. The present work indicates that this method is the most suitable technique for minimization of total potential energy function, especially in cases where the number of variables is large. The optimization of energy in the proposed theory achieves a decrease in computational time and in the number of iterations per time step.
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