W. A. M. Alwis

Wagner term in flexural-torsional buckling of thin-walled open-profile columns

This paper considers the Wagner term in flexural-torsional buckling of thin-walled open-profile columns, which has drawn much attention following its rejection by Ojalvo in 1981. During the ensuing debate on the subject, further issues of flexural-torsional buckling were raised highlighting the need for a comprehensive clarification. This paper collates various questions that have not been convincingly answered. In tackling these questions, two simple bar models are first used to clarify important differences between alternative representations of internal stress resultants, and their relationship with the Wagner term. With this background, a statically admissible free-body diagram is described, establishing the Wagner term without resorting to disputed means such as the use of a fictitious lateral load. The Wagner term is shown to be an internal stress resultant of the longitudinal prebuckling forces distributed across the member section; this stress resultant is of the same order of magnitude as the St Venant and warping torque. The spatial effect of stresses contributing to the Wagner term cannot be captured by the single line representation as proposed by Ojalvo.

Buckling of tapered circular plates: allowances for effects of shear and radial deformation

ABSTRACT Elastic axisymmeiric buckling of tapered circular plates under a compressive radial load is analyzed. The effects of shear and prebuckling radial deformation are considered in the analysis because they are important when plates are thick. No previous buckling data are known to exist for tapered circular plates with allowance for both of these effects. The buckling analysis is performed using the Rayleigh-Ritz method. The shooting method is used in the computation of the varying stress function along the plate radius. Comprehensive generic buckling results for circular plates with linearly or parabolically varying thickness are presented. It is noted that shear deformation tends to reduce the buckling load. However, this reduction in buckling load is somewhat offset by the strength-enhancing effect of prebuckling radial deformation that is smaller but of the same order of magnitude. Optimal taper parameter values for such tapered plates are obtained. It is found that the optimal taper is insensiti...

Discrete element slip model of plasticity

Abstract A two-dimensional domain under plane-stress conditions is considered. The admitted external loading comprises a unidirectional uniform body force and distributed forces along the boundary. By considering a discrete element slip model and applying the principle of virtual work, a comprehensive set of equilibrium equations purely in terms of the average shear stress along edges of a triangulated mesh in derived. Plastic collapse by incompressible flow due to shear failure at a limit stress can thereby be analyzed. The collapse mechanisms therein would contain tangentially discontinuous velocity fields. The coefficient of each shear stress term in the equilibrium equations is the sum of cotangents of two vertex angles in the mesh, whereas the coefficient of each boundary normal stress term is plus or minus unity. The number of internal nodes, boundary nodes and restrained boundary edges, together with the degree of connectivity of the domain, are adopted as primary quantifiers of the size of the numerical problem.

Should load remain constant when a thin-walled open-profile column buckles ?

Abstract This paper addresses the fundamental question of whether the applied load should necessarily be assumed to remain constant for bifurcation buckling analysis of thin-walled open-profile columns via the work-energy approach. The constant load condition has been recently used as a fundamental requirement for a valid analysis by Goto and Chen (1989, Int. J. Solids Structures 25 , 621–634) to dispute a theory proposed by Ojalvo (1989, ASME J. Appl. Mech . 56 , 633–638). This paper establishes that neither constant load nor constant distance need be insisted upon for a valid analysis. It is permissible to assume either constant load or constant distance (or any other compatible configuration with second order changes in loads and distance) for a valid analysis. It is essential to ensure that the appropriate strain energy and work expressions are adopted.

ON OPTIMAL ARCHGRIDS

Treated in this work is the optimality of flexureless orthogonal archgrids. Various features of fully stressed arches and archgrids are highlighted and an efficient and simple iterative method for obtaining the optimal solution is proposed. Considering the load proportions carried by arches as independent variables, the optimality of the archgrid is ensured by imposing the conditions of equal elevation at nodal intersections and individual optimality of component arches. Computational effort, is reduced by using a simple updating procedure during repetitive calculations. The convergence of the solution is aptly tested by the convergence of elevations and compressive forces in arches. It is shown that the optimal solutions for some skew archgrid systems can be obtained by solving equivalent orthogonal archgrids.