Nonlinear analysis of shear deformable beam-columns partially supported on tensionless three-parameter foundation

Abstract

In this paper, a boundary element method is developed for the nonlinear analysis of shear deformable beam-columns of arbitrary doubly symmetric simply or multiply connected constant cross-section, partially supported on tensionless three-parameter foundation, undergoing moderate large deflections under general boundary conditions. The beam-column is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as 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, to the axial displacement and to two stress functions and solved using the Analog Equation Method, a BEM-based method. Application of the boundary element technique yields a system of nonlinear equations from which the transverse and axial displacements are computed by an iterative process. 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 bending and shear deformations along the member as well as the shear forces along the span induced by the applied axial loading. Numerical examples are worked out to illustrate the efficiency, wherever possible, the accuracy and the range of applications of the developed method.

Force‐based derivation of exact stiffness matrix for beams onWinkler‐Pasternak foundation

“…Combining Eqs. (18) and (19) and considering the deformation-force relations of Eq. (6), the following relation between the first derivative of the shear-layer section shear force V s (x) and bending moment M (x) can be obtained as:…”

“…As a compromising way to represent the foundation medium, several subgrade models with different degrees of complexity have been used extensively to study the problems of beams on elastic foundation [13][14][15][16][17][18][19]. The Winkler foundation model [20] has been the simplest and most widely used subgrade model and is often referred to as the "one-parameter" foundation model.…”

“…It is noteworthy to mention that some researchers [26][27][28][29][30] formulated the two-parameter foundation model by first regarding the foundation as a semi-infinite continuum and then imposing some simplifications on displacement or/and stress variations within the foundation medium to arrive at the same expression of the foundation interactive force as those obtained by modifying the Winkler foundation model. It is also worthwhile to mention that several researchers [18,[31][32][33] had further improved the two-parameter foundation model by introducing a third foundation parameter to account for soil continuity as well as to determine the level of vertical-displacement continuity at the boundaries between the loaded and unloaded foundation surfaces, leading thus to the "three-parameter" foundation model.…”

Static interaction analysis between beam and layered soil using a two-parameter elastic foundation

“…Beam using Winkler foundation model (1867) is used in various practical problems. In this approach, the foundation flexibility is considered as a set of continuous springs and has employed to model soil-structure interaction (Kim and Yang 2010;Chore et al 2010;Sapountzakis and Kanpitsis 2011;Raychowdhury 2011;Limkatanyu et al 2012). Springs introduced provide a resistance in the vertical direction only confining the deformation of the soil foundation.…”

Static interaction analysis between a Timoshenko beam and layered soils by analytical layer element/boundary element method coupling

“…Based on the solution of the governing differential equation and the assumed displacement field, Onu [7,8] presented the stiffness matrices considering the shear effect of beams on two-parameter foundation. Sapountzakis and Kampitsis [9] developed a boundary element method to deal with the nonlinear behavior of a beam of shear deformation resting on a tensionless three-parameter foundation, in which the beam was partially supported on the foundation, and subjected to axial and transverse loads. Although spring foundation models are widely used in analyses of foundation beams, the shear effect of soils can not be properly considered in those models and the parameters may be difficult to obtain in practical engineering.…”