Thin-walled Structural Members Research Articles

Some recent research on thin-walled members at the University of Strathclyde

Details of some recent research projects on thin-walled structural members carried out at the University of Strathclyde are given in this paper. The projects are, in the main, short duration programmes carried out by students to examine various aspects of the behaviour of thin-walled members under various loadings. The topics consist of the effects of end fixity on plain channel column behaviour, the effects of transverse impact on struts and the damaged strut capacity and the large deflection behaviour of slender rings under diametrically opposed point loads.

Buckling stability of multilayer plates and shells with interfacial structural defects under axial compression

Based on the discrete-structural theory of thin plates and shells, a variant of the equations of buckling stability, containing a parameter of critical loading, is put forward for the thin-walled elements of a layered structure with a weakened interfacial contact. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is allowed over the interfaces between adjacent layers. The stability equations include the components of geometrically nonlinear moment subcritical buckling conditions for the compressed thin-walled elements. The buckling of two-layer transversely isotropic plates and cylinders under axial compression is investigated numerically and experimentally. It is found that variations in the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the magnitude of critical stresses. In solving test problems, a comparative analysis of the results of stability calculations for anisotropic plates and shells is performed with account of both perfect and weakened contacts between adjacent layers. It is found that the model variant suggested adequately reflects the behavior of layered thin-walled structural elements in calculating their buckling stability.

Measuring the cell wall mechanical properties of Al-alloy foams using the nanoindentation method

Abstract Al-foam is a super light weight material, promising for reinforcing thin-walled structural members in diverse engineering fields including aerospace and automobile industries. Measuring the material and mechanical properties (e.g. hardness and Young’s modulus of elasticity) of the cell wall of an Al-foam is a challenging task, as there are no standard methods available for such measurements. Nanoindentation is a method used for measuring the mechanical properties of thin films and surface layers, which is believed to be applicable for measuring the cell wall mechanical properties of Al-foams as well. However, there has been no detail investigation on applicability of nanoindentation measurements to cellular materials. In this paper, the nanoindentation technique has been used for measuring the cell wall mechanical properties of Al–Si–Cu–Mg alloy foams. The foams were produced using the powder metallurgical method. Hardness and elastic modulus of the specimens were evaluated using both the continuous stiffness measurement (CSM) and the unloading stiffness measurement (USM) method. Uni-axial tensile tests were performed on the precursor materials, and Vickers hardness of the specimens was measured. The experimental results revealed that the hardness and the elastic modulus of both the Al–3% (wt.)Si–2%Cu–2%Mg and the Al–5% (wt.)Si–4%Cu–4%Mg alloy foam cell walls are higher than those of their respective precursor materials. The elastic modulus obtained using the nanoindentation test was lower than that of the uni-axial tensile test. The hardness obtained using the nanoindentation method, however, was higher than the corresponding micro Vickers hardness. The average hardness of the foam cell wall was found to increase with the increase of foaming time regardless of the foaming temperatures and the alloy compositions.

854 前面および斜め衝撃荷重を受ける薄肉構造部材の動的圧潰特性(材料力学I)

854 前面および斜め衝撃荷重を受ける薄肉構造部材の動的圧潰特性(材料力学I)

Non-uniform torsion of stiffened open thin-walled members of steel structures

A general solution is derived, from distributional differential equations of equilibrium, for thin-walled structural members that are non-uniformly torsioned continuous, or situated in a Winkler rotational-elastic medium, with constant open cross-sections, stiffened with transversal ribs along their length. The equations were solved for a general case by means of the Laplace transform. Solutions were obtained in the form of closed generalized functions, holding good — for both non-uniform torsion displacements and internal forces and their influence lines — along the entire length of the bars. The effect of ribbing (diaphragms and closed ribs) on constrained torsion displacements and internal forces and on the respective influence lines is assessed for single-span and continuous I-section structural members. The results of non-uniform torsion tests carried out on I-bars stiffened along their length with battens or closed ribs (Fig. 12), in order to verify the theoretical models of the stiffened members (particularly with battens), are discussed. The test results confirmed the poor effectiveness of stiffeners in the form of battens directly joining the flanges of I-section members (Fig. 12(a)), due to the deformation of the flanges. The deformation can easily be eliminated by modifying the battens so that they join the flanges to the web (Fig. 12(b)). Tests showed that, by using the modified battens, one can effectively stiffen open thin-walled members. The effectiveness of the stiffening that is obtained is similar to that of stiffeners in the form of closed ribs.

Stress State of Multilayer Thin-Walled Elements with Interfacial Defects of Structure

Based on the discrete-structural theory of thin plates and shells, a calculation model for thin-walled elements consisting of a number of rigid anisotropic layers is put forward. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is allowed over the interfaces between adjacent layers. The solution to the problem is obtained in a geometrically nonlinear statement with account of the influence of transverse shear and compression strains. The stress-strain state of circular two-layer transversely isotropic plates, both without defects and with a local area of adhesion failure at their center, is investigated numerically and experimentally. It is found that the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the magnitude of stresses and strains. With the use of three variants of calculation models, in the cases of perfect and weakened contact conditions between layers, the calculation results for circular plates are compared. It is revealed that the variant suggested in this paper adequately reflects the behavior of layered thin-walled structural elements under large deformations.

衝撃軸圧縮荷重を受ける各種多角形薄肉断面構造部材の動的エネルギー吸収特性

衝撃軸圧縮荷重を受ける各種多角形薄肉断面構造部材の動的エネルギー吸収特性

Distortion of thin-walled beams

First order Generalized Beam Theory (GBT) describes the behaviour of prismatic thin-walled structural members by using system of ordinary differential equations. Solution can lead to separation of the load components and then to subsequent combination of the stresses and deformations. Application of GBT to a steel, cold-formed, thin-walled cantilever beam with complex non-symmetrical open cross section is presented. Theoretical values are compared with experimental ones.

Measurement Techniques in the Testing of Thin-Walled Structural Members

Measurement Techniques in the Testing of Thin-Walled Structural Members

Measurement Techniques in the Testing of Thin-walled Structural Members

Measurement Techniques in the Testing of Thin-walled Structural Members

Measurement techniques in the testing of thin-walled structural members

The paper describes methods for measuring displacements and end moments in the testing of thin-walled columns. The complete spatial deformation of a column can be captured by using local and overall deformation measurement frames. The local frame involves spring-loaded levers and roller bearings to mount the frame on to the specimen. The overall frame slides along high-precision shafts using linear ball bearings. Fixed-ended bearings are used to measure minor and major axis bending moments as well as the applied load. The bearings allow the line of action of the applied force to be determined.

Spectrotemporal analysis of guided-wave pulse-echo signals: Part 1. Dispersive systems

In this paper, a wavelet-based time frequency analysis is presented to analyze guided-wave signals for rapid inspection of thin-walled structural members. The overall objective is to detect and locate discontinuities using a single broadband signal. Part 1 of this paper shows how the wavelet transform can be used to analyze a dispersive system. A straightforward procedure is developed to extract group delay information from the computed wavelet transform coefficients. The procedure is demonstrated by a simulation study for single-mode and simple dual-mode dispersion signals. Part 2 is an experimental study of multimode dispersion.

Cyclic responses of thin-walled structural steel members subjected to three-dimensional loading

This paper presents an experimental investigation of the cyclic responses of thin-walled structural steel members under an earthquake-induced, coupled three-dimensional load. Nine thin-walled structural steel members were tested under various load combinations to investigate the correlation among bending, axial load and torsion. Bending capacities of tested members were compared to distinguish the effects of torsion, axial load and their combination in affecting a member's bending performance. Test results show that members' bending strength is reduced when axial load is applied. Further reduction in member performance is exhibited when coupled torsion and axial load are both present; this reduction demonstrates the necessity for including torsion in calculating a member's bending strength when buildings are designed to be earthquake-resistant.

Guided Waves in Thin-Walled Structural Members

A semi-analytical finite element (SAFE) formulation is proposed to study the wave propagation characteristics of thin-walled members with an infinite length in the longitudinal (axial) direction. Common structural members are considered as an assemblage of thin plates. The ratio of the thickness of the plate to the wavelength in the axial direction is assumed to be small so that the plane-stress assumption is valid. Employing a finite element modeling in the transverse direction circumvents difficulties associated with the cross-sectional profile of the member. The dynamic behavior is approximated by dividing the plates into several line (one-dimensional) segments and representing the generalized displacement distribution through the segment by polynomial interpolation functions. By applying Hamilton’s principle, the dispersion equation is obtained as a standard algebraic eigenvalue problem. The reasonably good accuracy of the method is demonstrated for the lowest modes by comparing, where feasible, the results with analytical solutions. To demonstrate the method’s versatility, frequency spectra are also presented for I and L shaped cross sections.

Design sensitivity of post-buckling states including material constraints

This paper reports theoretical studies on the design sensitivity of problems with geometrically non-linear behavior leading to buckling and post-buckling of thin-walled structural members. For the class of problems considered, buckling occurs in the form of a stable bifurcation, and it is assumed that changes in the design parameters do not break the bifurcation behavior. The specific focus of the research is the first yield or first failure of the material as part of the sensitivity study of equilibrium states along the post-critical path. The investigation employs a discrete model of a structure in terms of generalized coordinates (suitable for finite element analysis) and a single load parameter; and perturbation techniques to classify the critical state and to approximate the post-critical path. The problem of material behavior is modeled by means of constraints on the post-critical path, based on a yield criterion. For simplicity, the presentation uses the von Mises yield criterion, but other more complex criteria, such as those employed in composite materials (first-ply failure) can also be represented. Two forms of the constraints are formulated, and the problem of sensitivity with respect to changes in a design parameter is discussed. A simple example of a circular plate is presented to illustrate the use of the formulation for the sensitivity with respect to a single design parameter.

Explicit stability conditions for integro-differential equations with periodic coefficients

New explicit stability conditions are derived for a linear integro-differential equation with periodic operator coefficients. The equation under consideration describes oscillations of thin-walled viscoelastic structural members driven by periodic loads. To develop stability conditions two approaches are combined. The first is based on the direct Lyapunov method of constructing stability functionals. It allows stability conditions to be derived for unbounded operator coefficients, but fails to correctly predict the critical loads for high-frequency excitations. The other approach is based on transforming the equation under consideration in such a way that an appropriate ‘differential’ part of the new equation would possess some reserve of stability. Stability conditions for the transformed equation are obtained by using a technique of integral estimates. This method provides acceptable estimates of the critical forces for periodic loads, but can be applied to equations with bounded coefficients only. Combining these two approaches, we derive explicit stability conditions which are close to the Floquet criterion when the integral term vanishes. These conditions are applied to the stability problem for a viscoelastic bar compressed by periodic forces. The effect of material and structural parameters on the critical load is studied numerically. © 1998 B. G. Teubner Stuttgart–John Wiley & Sons Ltd.

Flux distributions near boundaries of magnetizable shells

The singular behavior of magnetic fields near the boundary curves of thin-walled structural members such as soft ferromagnetic plates or open shells is explored. Employing the concept of magnetic surface flux and results from potential theory, together with some reasonable assumptions concerning modeling and nonlinear magnetizability, explicit expressions and field plots are obtained. The paper includes a discussion on "forces of magnetic origin" in the present context.

Feasibility Study of a Torsional-Bending Piezoelectric Actuator

The objective of this paper is to show the feasibility of a novel actuator capable of inducing torsional, bending and longitudinal control loads in a thin-walled structural member using piezoelectric elements. Torque is generated by extension/compression action of a set of piezoelectric elements surface bonded to the walls of a structural element. The same set of elements may be used to control torsional, bending and longitudinal vibrations. Analytical and experimental validations of the concept are presented.

Computer analysis of thin-walled structural members

The calculation of the stresses and failure modes in thin-walled structural members is a complex procedure. Structural designers will often need help in analysing these types of structures. A vehicle for providing this help is the computer program developed for the microcomputer. In this paper, a computer procedure is described for the cross-section analysis and elastic buckling analysis of thin-walled structural members. The cross-section analysis calculates the section properties, warping displacements, and the longitudinal and shear stresses for thin-walled open and closed cross-sections of any shape. The longitudinal stresses are used to perform an elastic finite strip buckling analysis of thin-walled structural members. The analysis can be done for a number of different buckle half-wavelengths of the member and the load factor and buckled shape are output for each length. The analysis is performed by the user-friendly computer program THIN-WALL, which is also described in the paper.

Combination resonance of thin-walled structural members subjected to periodic axial follower torque and force

Abstract The basic equation of motion of structural members with a thin-walled cross-section under periodic follower torque and force becomes a Mathieu’s equation and simple parametric and combination resonances occur in this system. The regions of those resonances of the members with various boundary conditions are estimated by using the stability criterion with the characteristic exponent and their instability becomes evident from the numerical results.