A modal superposition method for analyzing nonlinear structural dynamic problems involving impact between components is developed and evaluated. The finite-element method is used to express the equations of motion with nonlinearities represented by pseudo force vector. Three test problems are solved to verify this method. This has demonstrated the applicability of this method to seismic analysis of large, complex structural systems. It is concluded that the modal superposition method has a significant cost advantage over the direct integration method for problems with large wave fronts and the source of nonlinearities restricted to a limited portion of the structure.
Modal Superposition Method for Computationally Economical Nonlinear Structural Analysis
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Shah, V. N., Bohm, G. J., and Nahavandi, A. N. (May 1, 1979). "Modal Superposition Method for Computationally Economical Nonlinear Structural Analysis." ASME. J. Pressure Vessel Technol. May 1979; 101(2): 134–141. https://doi.org/10.1115/1.3454612
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