Nonlinear Dynamic Analysis of Shear Deformable Beam-Columns on Nonlinear Three-Parameter Viscoelastic Foundation. I: Theory and Numerical Implementation

Abstract

A boundary element method is developed for the nonlinear dynamic analysis of beam-columns of an arbitrary doubly symmetric simply or multiply connected constant cross section, partially supported on a nonlinear three-parameter viscoelastic foundation, undergoing moderate large deflections under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. Part I is devoted to the theoretical development and numerical implementation of the method, while Part II discusses the examined numerical appli- cations illustrating the efficiency (wherever possible), the accuracy, and the rangeof applicationsof theproposedmethod. The beam-column is subjectedtothecombinedactionofarbitrarilydistributedorconcentratedtransverseloadingandbendingmomentsinbothdirections,aswellas to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary-value problems are formulated with respect to the transverse displacements, axial displacement, and two stress functions, and solved using the analog equation method, a boundary elementebased method. Application of the boundary element technique yields a nonlinear coupled system of equations of motion. The solution to this system is accomplished iteratively by employing the average acceleration method in combination with the modified Newton-Raphson method. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. The proposed model takes into account the coupling effects of the bending and shear deformations along the member as well as the shear forces along the span induced by the applied axial loading. DOI: 10.1061/(ASCE)EM.1943- 7889.0000369. © 2013 American Society of Civil Engineers. CE Database subject headings: Nonlinear analysis; Deflection; Beam columns; Shear deformation; Coefficients; Boundary element method; Viscoelasticity; Elastic foundations. Author keywords: Nonlinear dynamic analysis; Large deflections; Timoshenko beam; Shear deformation coefficients; Boundary element method; viscoelastic foundation; Nonlinear foundation.