Thin-walled Frames Research Articles

Large-Displacement Analysis of Elastoplastic Thin-Walled Frames. I: Formulation and Implementation

This paper presents a new formulation for the large-displacement analysis of thin-walled frames taking into account the effects of elastoplastic material behavior. The proposed formulation is derived in an Eulerian (convected) local system which allows relatively simple strain-displacement relationships to be used. Furthermore, the formulation uses the fiber approach for representing the spread of plasticity over a general open cross section, and is capable of modeling initial imperfections, residual stresses, and the Wagner effect. In accounting for material plasticity effects, consideration is given to the interaction between normal stresses and shear stresses due to twisting. Since the shear strain is directly related to the rate of twist, the shear stress in the yield function is replaced by an equivalent contribution to the cross-sectional torque, which leads to considerable computational advantages. This paper describes the formulation details and the implementation of material plasticity effects for kinematic and isotropic strain hardening, whereas the companion paper provides a number of verification and application examples.

Large-Displacement Analysis of Elastoplastic Thin-Walled Frames. II: Verification and Application

The companion paper presents a new Eulerian formulation for the large-displacement analysis of thin-walled frames, accounting for the elastoplastic material response. This paper aims at verifying the proposed formulation and providing several examples of its application ot thin-walled members and frames. In this regard, it is demonstrated that such a relatively simple formulation enables the accurate modeling of initial imperfections, residual stresses, the Wagner effect, the beam-column effect, lateral-torsional instability, and large displacements using a small number of elements and a coarse cross-sectional discretization. Moreover, it is shown that the formulation can be used in the assessment of the ultimate and postultimate response of thin-walled structures for which the design codes are either inaccurate or inapplicable. Such structures include continuous beams, simply supported beams with intermediate lateral restraints, as well as frames for which the ultimate limit state involves considerable interaction between the structural members.

Analysis and tests of flexibly connected thin-walled channel frames

The analysis and tests of thin-walled channel frames including nonlinear flexible or semi-rigid connection behaviour is presented. The semi-rigid connection behaviour is modelled using a mathematical approximation of the connection flexibility-moment relationship. Local instability such as local buckling and torsional flexural buckling of the member are included in the analysis. The full response of the frame, up to the collapse load, can be predicted. Experimental investigation was carried out on a series of simple double storey symmetrical frames with the purpose of verifying the accuracy and validity of the analysis. Agreement between the theoretical and experimental results is acceptable. The investigation also shows that connection flexibility and local instability such as local buckling and torsional flexural buckling can affect the behaviour and strength of thin-walled frames significantly. The results can also provide further insight into the advanced study of practical structures where interaction between flexible connections and phenomenon associated with thin-walled members are present.

Nonlinear Vibrations of Thin-Walled Composite Frames

A reduced basis technique and a computational procedure are presented for generating the nonlinear vibrational response, and evaluating the first-order sensitivity coefficients of thin-walled composite frames. The sensitivity coefficients are the derivatives of the nonlinear frequency with respect to the material and lamination parameters of the frame. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frame. The flanges and webs of the frames are modeled by using geometrically nonlinear two-dimensional shell and plate finite elements. The computational procedure can be conveniently divided into three distinct steps. The first step involves the generation of various-order perturbation vectors, and their derivatives with respect to the material and lamination parameters of the frame, using the Linstedt–Poincaré perturbation technique. The second step consists of using the perturbation vectors as basis vectors, computing the amplitudes of these vectors and the nonlinear frequency of vibration, via a direct variational procedure. The third step consists of using the perturbation vectors, and their derivatives, as basis vectors and computing the sensitivity coefficients of the nonlinear frequency via a second application of the direct variational procedure. Numerical results are presented for semicircular thin-walled frames with I and J sections, showing the convergence of the nonlinear frequency and the sensitivity coefficients obtained by both the reduced-basis and perturbation techniques.

Nonlinear Vibrations of Thin-Walled Composite Frames

A reduced basis technique and a computational procedure are presented for generating the nonlinear vibrational response, and evaluating the first-order sensitivity coefficients of thin-walled composite frames. The sensitivity coefficients are the derivatives of the nonlinear frequency with respect to the material and lamination parameters of the frame. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frame. The flanges and webs of the frames are modeled by using geometrically nonlinear two-dimensional shell and plate finite elements. The computational procedure can be conveniently divided into three distinct steps. The first step involves the generation of various-order perturbation vectors, and their derivatives with respect to the material and lamination parameters of the frame, using the Linstedt–Poincare perturbation technique. The second step consists of using the perturbation vectors as basis vectors, computing the amplitudes of these vectors and the nonlinear frequency of vibration, via a direct variational procedure. The third step consists of using the perturbation vectors, and their derivatives, as basis vectors and computing the sensitivity coefficients of the nonlinear frequency via a second application of the direct variational procedure. Numerical results are presented for semicircular thin-walled frames with I and J sections, showing the convergence of the nonlinear frequency and the sensitivity coefficients obtained by both the reduced-basis and perturbation techniques.

HARMONIC FINITE-ELEMENT THERMOELASTIC ANALYSIS OF SPACE FRAMES AND TRUSSES

A numerical procedure is devised for the thermoelastic analysis of three-dimensional frame- or truss-type space structures exposed to solar radiation. Thin-walled frame or truss members with cross sections of arbitrary shape are considered. Tension-compression, bending, shear, and torsional effects due to the temperature distribution induced by the solar radiation are all taken into account. The procedure proposed involves finite element discretization in the axial direction and a harmonic analysis in the circumferential direction of each member. This procedure is an extension of the one employed previously to obtain the temperature field in trusses. A multibay frame structure serves as a model to demonstrate the performance of the proposed method. The temperature, displacement, and stress fields in the frame are found in various cases.

Natural approach for geometric non‐linear analysis of thin‐walled frames

Natural approach for geometric non‐linear analysis of thin‐walled frames

Free vibrations of thin-walled semicircular graphite-epoxy composite frames

A detailed study is made of the effects of variations in lamination and material parameters of thin-walled composite frames on their vibrational characteristics. The structures considered are semicircular thin-walled frames with I and J sections. The flanges and webs of the frames are modeled by using two-dimensional shell and plate finite elements. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frame. The frequencies and modes predicted by the two-dimensional finite-element model are compared with those obtained from experiments, as well as with the predictions of a one-dimensional, thin-walled-beam, finite-element model. A detailed study is made of the sensitivity of the vibrational response to variations in the fiber orientation, material properties of the individual layers, and boundary conditions.

Impact response of thin-walled frame structures

This paper describes a finite-element method which was developed to predict the impact response of three-dimensional thin-walled frame structures. The softening effect of the load-deformation characteristics for thin-walled beams under combined axial compression, bending and torsional loads during impact is simulated by making use of a nonlinear Maxwell model. The large deformation of a structure is calculated by using updated nodal coordinates and internal forces, and the flexibility matrix for a curved beam element. Crash tests against a flat barrier were made on three-dimensional frame models. Comparisons between the calculated and experimental force-time relations and the deformed shape of the frame are discussed.

Nonlinear buckling analysis of two-dimensional frames composed of curved non-prismatic members

A novel finite element methodology is presented for the analysis of arbitrarily shaped two-dimensional frames composed of curved non-prismatic members. The method utilizes a hybrid-mixed approach in conjunction with an updated Lagrangian formulation. The proposed methodology goes beyond existing modelling capabilities for it enables a more realistic analysis of the nonlinear response of thin-walled frames undergoing large deflections (displacements and/or rotations) in the pre- and postbuckling range. Efficiency, accuracy and reliability of the proposed method are demonstrated on the basis of numerical experiments carried out on several typical examples.

Geometrically and materially nonlinear finite element analysis of thin-walled frames: Numerical studies

This paper deals with the finite element analysis of free-form beams and frames undergoing large elastoplastic deformations. A mixed hybrid model proposed previously implemented and tested on a series of well selected examples representing a broad range of circumstances in non-linear beam and frame analysis.

On the importance of cross-sectional flexibility on gross response

Most nonlinear analyzers like ACTION and PLANS do not account for cross-sectional flexibility of thin-walled frame members. They do however, permit simulation of plastic hinges. Judging by the excellent correlation between theory and experiment, such analyzers appear quite adequate in predicting reasonably accurately gross response parameters of thin-walled frame structures even though they may undergo severe cross-sectional deformations.

Closure to “Large-Deflection Spatial Buckling of Thin-Walled Beams and Frames”

Closure to “Large-Deflection Spatial Buckling of Thin-Walled Beams and Frames”

Discussion of “Large-Deflection Spatial Buckling of Thin-Walled Beams and Frames”

Discussion of “Large-Deflection Spatial Buckling of Thin-Walled Beams and Frames”

Minimum Weight Design of Thin–walled Cells in Torsion

The minimum weight approach to structural design was introduced by F. R. Shanley with reference to narrow and wide columns and shells subjected to bending, and was later dealt with more comprehensively in a book by the same author. This was further extended to structures like tapered round thin-walled columns and frames. In this paper expressions giving optimum sectional dimensions for long thin walled cells of circular, semi–circular, rectangular and triangular shapes and uniform wall thickness have been derived. The design criteria used to obtain the minimum necessary conditions are (1) failure by local buckling and (2) a limit on the twisting deformation of the cells. Working curves from which the optimum sectional dimensions can be read for given torque and limiting twist have been plotted. And finally, a method of approach to the problem of combined bending and torsion has also been indicated.