In-plane Bending Behavior Research Articles

Influence of in-plane bending behaviour on textile composite reinforcement forming

The deformation of textile composite reinforcement is influenced by its fibrous composition. In-plane bending behaviour is an inherent aspect of textile reinforcement, yet it is frequently overlooked. The paper elucidates the significant influence of in-plane bending behaviour on fibre orientation during forming process and emphasizes the necessity of accounting for in-plane bending virtual work to prevent non-physical deformation mode. To this purpose in-plane bending calculation is implemented into a fibrous shell finite element by using the neighbouring elements method. Numerical spurious mode involving in-plane shear is avoided due to the new approach. Finally, the model is validated by comparing with composite reinforcement draping experiments: fibre orientations and distributions of shear angles are simulated in good agreement with experiments and give better results than the simulations neglecting the in-plane bending behaviour.

Experimental and Numerical Flexural–Torsional Performance of Thin-Walled Open-Ended Steel Vertical Pile Foundations Subjected to Lateral Loads

This research investigates the effects of torsional moments on the mechanical behavior of thin-walled open-ended vertical pile foundations subjected to lateral wind loads. The aim of this research is to determine and quantify the errors using traditional design methods and provide more effective alternatives. The warping and torsion effect generated over the piles due to the resultant lateral load impact outside the shear center is analyzed in field tests. Complementarily, a two-dimensional finite element model based on the simple bending stress–strain state, as well as a three-dimensional finite element model considering torsional effects, were implemented and their results analyzed. Finally, a comparative analysis between the in-field lateral loading tests and the finite element model approaches was established by comparing load–displacement curves and using a non-linear Wrinkle model of the soil. Additionally, correlations between the experimental and finite element model errors for the cross-sections pile with a different torsional constant and torsional susceptibility index are shown. From the results, it has been ascertained that the slender thin-walled open-ended pile foundations are particularly sensitive to small load deviations from their center of gravity; this leads to the fact that the slenderer the load and the greater its eccentricity, the more it affects the torsion and warping of the pile. Calculation methodologies usually consider a simple in-plane bending behavior, which leads to errors between 44 and 58% in comparison with the experimental results obtained.

In-plane bending behaviour and capacities of S690 high strength steel welded I-section beams

The present paper describes an in-depth experimental and numerical investigation into the in-plane flexural behaviour and bending moment capacities of S690 high strength steel welded I-section beams. The experimental investigation was conducted on six different welded I-sections fabricated from the same batch of 5 mm thick S700MC high strength steel hot-rolled plates by means of gas metal arc welding, and involved initial local geometric imperfection measurements and twelve in-plane four-point bending tests, with six performed about the cross-section major principal axes and another six conducted about the cross-section minor principal axes. Following the experimental study, a numerical investigation was performed, where the developed finite element models were firstly validated against the test results and then used to perform parametric studies to generate further structural performance data over a broader range of cross-section sizes. The obtained experimental and numerical results were carefully analysed and then adopted to evaluate the accuracy of the existing slenderness limits (for classifications of plate elements and cross-sections) and local buckling design rules for S690 high strength steel welded I-sections in bending, as set out in the European, Australian and American standards. The results of the evaluation revealed that the codified slenderness limits are generally safe when used for the classification of the constituent plate elements of the examined S690 high strength steel welded I-section beams, except for that given in the American specification for slender/non-slender outstand elements in compression. All of the three considered design standards were shown to yield accurate cross-section bending moment capacity predictions for compact (Class 1 and 2) S690 high strength steel welded I-section beams bent about both the principal axes and non-compact (Class 3) S690 high strength steel welded I-section beams bent about the major principal axes, but resulted in a rather high level of conservatism in predicting the cross-section bending moment capacities for non-compact (Class 3) S690 high strength steel welded I-sections in bending about the minor principal axes and slender (Class 4) S690 high strength steel welded I-sections subjected to both major-axis bending and minor-axis bending.

In-plane flexural behaviour and failure prediction of carbon fibre-reinforced aluminium laminates

This paper investigated the in-plane bending behaviour of carbon fibre-reinforced aluminium laminates (CARALL). The flexural progressive damage and failure mechanisms were analysed numerically and experimentally. Four types of CARALL specimens with a 3/2 configuration were prepared via hot-pressing using different aluminium alloy materials (2024-T3, 7075-T6 aluminium alloy) and fibre orientations ([0°/90°/0°]3, [45°/0°/−45°]3). The three-point bending tests were conducted under static loading. It was found that the primary damage modes were aluminium layer yielding in the mid-span and delamination between the aluminium and carbon fibre-reinforced polymer (CFRP) layers. A user-defined FORTRAN subroutine VUMAT based on ABAQUS was used to simulate the failure of the CFRP, a cohesive zone model was used to predict the inter-laminar failure, and a von Mises plastic model was used to define the isotropic hardening behaviour of the aluminium layers. The predicted results agreed well with the experimental ones. Two convenient calculation methods based on the elasticity mechanics and material mechanics were derived. And the non-linear behaviour of aluminium was considered in the elasticity mechanics method. The theoretical results matched closely with the experimental findings during the linear elastic deformation process.

Flexural behavior of in-plane bending glass structures for design method

Experimental study was carried out on the in-plane bending behavior of glass plates without lateral supports, and the effects of the factors, such as height-to-span ratio, on the stability of glass panels were studied. Results show that the in-plane bending glass plates with both ends simply supported and their upper edge free lose overall stability under loads, which belongs to the limit-point type of instability. It is found that the buckling load increases linearly with the increase of height-to-span ratio of the glass plates. The lateral stress of in-plane bending glass plates without lateral supports increases linearly under loads; while the large-area stress increases nonlinearly and the lateral stress is not the controlling factor of instability. In finite element analysis, the first buckling mode is regarded as the initial imperfection and imposed on the model as 1/1000 of the span of the components. The numerical buckling load according to the theory of large deflection is less than the experiment result, which is more conservative and can provide some reference for design. For the design method, when the in-plane load is imposed on the glass plate, its lateral strength and the deflection should be verified. Considering the stability of the in-plane bending glass plate without reliable lateral support, buckling is another possible failure mode and calls for verification.

Behavior of Corrugated Web I-Girders under In-Plane Loads

A theoretical formulation of the linear elastic in-plane and torsional behavior of corrugated web I-girders under in-plane loads is presented. A typical corrugated web steel I-girder consists of two steel flanges welded to a corrugated steel web. Under a set of simplifying assumptions, the equilibrium of an infinitesimal length of a corrugated web I-girder is studied, and the cross-sectional stresses and stress resultants due to primary bending moment and shear are deduced. The analysis shows that a corrugated web I-girder will twist out-of-plane simultaneously as it deflects in-plane under the action of in-plane loads. In the paper, the in-plane bending behavior is analyzed using conventional beam theory, whereas the out-of-plane torsional behavior is analyzed as a flange transverse bending problem. The results for a simply supported span subjected to a uniformly distributed load are presented. Finally, finite element analysis results are presented and compared to the theoretical results for validation.

A family of piezoelectric MITC plate elements

In the present paper, a class of accurate and reliable piezoelectric plate elements is presented. The formulations are based upon the Reissner–Mindlin assumptions, which makes the elements applicable to both thin and moderately thick situations. Shear locking is eliminated by employing the MITC (mixed interpolation of tensorial components) approach for the transverse shear strains. To improve the in-plane bending behaviour in the four node elements, incompatible modes are used. Regarding the assumptions for the electric field, it is shown that only a quadratic variation of the electric potential over the thickness can take into account the potential induced by the bending deformation. Two different approaches are developed that fulfil this requirement. The first formulation is based upon an analytical integration of the electric charge equation over the plate thickness, using the kinematic assumptions of the Reissner–Mindlin theory. As compared to elastic plate elements, only one additional global degree of freedom is introduced for every electrode pair, which makes the formulation very efficient. The second formulation interpolates the electric potential over the thickness, employing additional electric degrees of freedom at the mid-plane nodes. This approach is computationally more expensive than the first one, but allows a more accurate modelling of the in-plane electric field. The resulting elements are very widely applicable and can be used for both sensing and actuation. A number of numerical examples are given to compare the two approaches and demonstrate the elements’ performance.

Assumed stress formulation of high order quadrilateral elements with an improved in-plane bending behaviour

The paper proposes two quadrilateral finite elements for the analysis of plane elastic problems. The elements are designed to obtain a mechanical response characterized by improved in-plane bending behaviour, a response which is difficult to obtain by the usual compatible elements. The adopted assumed stress approach enables either an easy formulation of the elements or a careful tuning of the desired mechanical response. The proposed elements behave well in classical numerical tests and are suitable for use with rough meshes.

Adaptive multi-point quadrature for elastic–plastic shell elements

A multi-point integration scheme to enhance the coarse-mesh accuracy of the four-node quadrilateral shell element for elastic–plastic simulations by explicit methods is described. Compared to 1-point quadrature elements, considerably improved results can be obtained by using this multi-point scheme in beam bending problems where a model with one or two layers of elements along the depth is employed. In the interest of efficiency, an adaptive scheme is devised in which the number of quadrature points depends on the state of the element. This speeds up the computation and maintains accuracy in the plastic range. The scheme is designed so that no incompatibility is introduced upon switching from 1-point to multi-point quadrature. The speed-up achieved by adaptive quadrature depends on problem parameters. Numerical examples show that this adaptive quadrature method effectively captures the in-plane bending behavior in elastic–plastic simulations and achieves good efficiency.

Extrapolated fields in the formulation of the assumed strain elements Part 1: Two-dimensional problems

A new assumed strain quadrilateral element with accurate in-plane bending behavior is presented. The basic idea consists in introduction of a parallelogram domain associated with the given quadrilateral element, development of the related assumed strain field for the parallelogram, and subsequent extrapolation of this field to the domain of the original quadrilateral. The assumed strain field for the parallelogram is constructed by identification of various modes of its deformation and then by proper modification of the strain field in some of these modes. In particular, the strain operator with respect to the so-called in-plane bending modes is modified so as to simulate the strain field resulting from the assumptions usually made in structural mechanics. The modification of the strain fields leads to the assumed strain operator.The proposed new assumed strain quadrilateral element exhibits remarkably accurate performance for both membrane and bending dominated problems even when severely distorted and high aspect ratio meshes are considered and when materials are nearly incompressible.

In-Plane Bending Behavior of Pipe Bends With End Constraints Under Steady-State Creep

This paper presents an analysis for the in-plane bending behavior of smooth thin pipe bends connected to tangent pipes or rigid flanges under steady-state creep conditions. Creep flexibility factors obtained from this analysis are presented and compared with earlier results from existing theories with no end constraints. Applications to design are briefly discussed.

In-plane bending of elbows

This paper presents a finite element analysis of the in-plane bending behavior of elastic elbows. Rules and guidelines are presented for the systematic selection of the dimensions of the finite element meshes and for the interpretation of the numerical results. A simple asymptotic formula is presented that gives the dimensions of a so-called “optimum” (or “upper bound”) mesh as a function of the geometry of the elbow. This mesh, along with a companion one, the “lower bound” mesh, serve to establish the basis for the selection of the range of mesh dimensions that are used in the convergence studies of the MARC finite element computations for stresses, displacements and stress intensification and flexibility factors appropriate to a typical FFTF elbow. Reasonable good agreement is found in a comparison of the MARC results with those obtained from the ELBOW computer program, as well as with results predicted by Clark and Reissner's asymptotic formulas.