Buckling Analysis Of Thin-walled Members Research Articles

Constrained shell finite element method for elastic buckling analysis of thin-walled members

Abstract The objective of this paper is to develop a constrained shell Finite Element Method (cFEM) based on a force approach for elastic buckling analysis of thin-walled members. The new cFEM is able to separate the general deformation of thin-walled members into the three fundamental deformation mode classes, namely Global (G), Distortional (D), and Local (L), to enable the modal decomposition and identification. In this paper, four force-based mechanical criteria are defined to separate these mode classes. These mechanical criteria are implemented with the general shell finite element formulation without any special treatment of the element formulation. The constraint matrices of the G, D, and L mode classes are then constructed. Numerical examples are presented to demonstrate the capabilities of the new cFEM in modal decomposition and identification. In particular, the modal decomposition and identification results are compared with the cFSM solutions. Applicability of the new cFEM to other shell FE formulation and different loading conditions are illustrated. All these numerical examples demonstrate the potential of the developed cFEM in taking advantages of the modeling capability of the existing shell FE method.

Modal buckling analysis of thin-walled members with rounded corners by using the constrained finite strip method with elastic corner elements

In this paper modal decomposition of thin-walled structural members with rounded corners is discussed. Modal decomposition is a process which separates the characteristic behaviour types. If modal decomposition is applied in buckling analysis, pure uncoupled buckling modes can readily be analysed, such as pure global buckling, pure distortional buckling or pure local-plate buckling. Ability to calculate critical loads to a pure buckling mode is highly beneficial in the design of thin-walled structural members, for example in the design of cold-formed steel beams or columns. However, cold-formed steel profiles are always produced with rounded corners, and earlier studies showed that the now-used modal decomposition techniques of the constrained finite strip/element method sometimes fail to lead to reasonable results if the rounded corners are directly modelled in the analysis. In this paper a special version of the constrained finite strip method is presented and discussed. The proposed method introduces elastic corner elements, which makes it possible to perform the modal decomposition by the same process used for members with sharp corners, even if the rounded corners are directly modelled, still the results of pure buckling modes satisfy the engineering expectations. The theoretical background of the proposal is briefly summarized, then the elastic-corner approach is discussed by detailed analysis of sample examples as well as by an extended parametric study.

Constrained shell Finite Element Method, Part 2: application to linear buckling analysis of thin-walled members

In this paper a novel method is employed for the buckling analysis of thin-walled members. The method is basically a shell finite element method, but constraints are applied which enforce the thin-walled member to deform in accordance with specific mechanical criteria, e.g., to force the member to buckle in flexural, or lateral-torsional or distortional mode. The method is essentially similar to the constrained finite strip method, but the trigonometric longitudinal shape functions of the finite strip method are replaced by polynomial longitudinal shape functions, and longitudinal discretization is used, which transform the finite strip into multiple finite elements, that is why the new method can readily be termed as constrained (shell) finite element method. In the companion to this paper a band of finite elements is discussed in detail, where ‘band’ is a segment of the member with one single finite element longitudinally. In this paper the constraining procedure is applied on thin-walled members discretized both in the transverse and longitudinal direction. The possible base systems for the various deformation spaces are demonstrated here, as well as numerous buckling examples are provided to illustrate the potential of the proposed method.

Upper and lower bound solutions for lateral-torsional buckling of doubly symmetric members

A family of three finite elements is developed for the lateral-torsional buckling analysis of thin-walled members with doubly symmetric cross-sections. The elements are based on a recently derived variational principle which incorporates shear deformation effects in conjunction with a special interpolation scheme ensuring C1 continuity. One of the elements is developed such that it consistently converges from above while another element is intended to consistently converge from below. The third element exhibits fast convergence characteristics compared to other elements but cannot be guaranteed to provide either an upper or a lower bound solution. The formulation incorporates the ability to enforce any set of linear multi-point kinematic constraints. The validity of the solution is established through comparisons with other well-established numerical solutions. The elements are then used to solve practical problems involving simply supported beams, cantilevers and continuous beams under a variety of loading conditions including concentrated loads, linear bending moments and uniformly distributed loads. The effect of lateral and torsional restraints and the location of lateral restraint along the section height on lateral-torsional buckling capacity of beams are also examined through examples.

Linear buckling analysis of thin-walled members combining the Generalised Beam Theory and the Finite Element Method

A finite element procedure to carry out linear buckling analysis of thin-walled members is developed on the basis of the existing Generalised Beam Theory (GBT) and constrained Finite Strip Method (cFSM). It allows designers to uncouple the buckling modes of a finite element model and, consequently, to calculate pure elastic buckling loads. The procedure can easily be applied to members with general boundary conditions subjected to compression or bending. The results obtained are rather accurate when compared to the values calculated via GBT and cFSM. As a consequence, it is demonstrated that linear buckling analyses can be performed with the Finite Element Method in a similar way as can be done with the existing GBT and cFSM procedures.

GBT-based buckling analysis of thin-walled members with non-standard support conditions

This paper reports on the use of a recently developed Generalised Beam Theory (GBT) formulation, and corresponding finite element implementation, to analyse the local and global buckling behaviour of thin-walled members with arbitrary loading and support conditions — this formulation takes into account longitudinal normal stress gradients and the ensuing pre-buckling shear stresses. After presenting an overview of the main concepts and procedures involved in the performance of a GBT-based (beam finite element) member buckling analysis, one addresses in detail the incorporation of non-standard support conditions, such as (i) full or partial localised displacement or rotation restraints, (ii) rigid or elastic intermediate supports or (iii) end supports corresponding to angle connections. In order to illustrate the application and capabilities of the proposed GBT-based approach, one presents and discusses numerical results concerning cold-formed steel (i) lipped channel beams and (ii) lipped I-section beams and columns with various “non-standard” support conditions — while the beams are acted by uniformly distributed or mid-span point loads, applied at the shear centre axis, the columns are subjected to uniform compression. In particular, it is possible to assess the influence of the different support conditions on the beam and column buckling behaviour (critical buckling loads and mode shapes). For validation purposes, most GBT-based results are compared with values yielded by shell finite element analyses carried out in the code A nsys.

Lateral buckling of thin-walled members with shear lag using spline finite member element method

Based on the displacement variational principle, a general method, called the spline finite member element method, is developed for lateral buckling analysis of thin-walled members. A transformed B 3-spline function presented in the paper is used to simulate the longitudinal warping displacement field along the cross section of the thin-walled member. The analysis takes into account the effect of shearing strains of the middle surface of walls on the buckling, which reflects the shear lag phenomenon. Compared with the results from classical theory and other methods, the numerical results proposed in the paper demonstrate the versatility, accuracy and efficiency of the proposed method. The fast convergency, shown in numerical examples, predicts the reliability of the results.