Predicting wheel forces using bearing capacity theory for general planar loads

A numerical method for the topological design of periodic continuous domains under general loading is presented. Both the analysis and the design are defined over a single cell. Confining the analysis to the repetitive unit is obtained by the representative cell method which by means of the discrete Fourier transform reduces the original problem to a boundary value problem defined over one module, the representative cell. The repeating module is then meshed into a dense grid of finite elements and solved by finite element analysis. The technique is combined with topology optimization of infinite spatially periodic structures under arbitrary static loading. Minimum compliance structures under a constant volume of material are obtained by using the densities of material as design variables and by satisfying a classical optimality criterion which is generalized to encompass periodic structures. The method is illustrated with the design of an infinite strip possessing 1D translational symmetry and a cyclic structure under a tangential point force. A parametric study presents the evolution of the solution as a function of the aspect ratio of the representative cell.

A low-floor train–turnout coupling dynamic model considering bad alignment irregularity ahead of the turnout was established on the basis of a field test in which the dynamic performances of a low-floor train passing through a no. 6 turnout in a rail transit depot in China had been measured, as well as the line alignment and wheel and rail profiles. There are two types of wheelsets in the low-floor train: integral wheelset and independent wheelset. The model fully considers the coupling effect between the vehicle and the ballast components, and the simulated results are in consistence with measured results in the field test. Based on this, the influences of train speed, the wheel–rail friction coefficient, and the track alignment optimization of the dynamic performance of low-floor trains passing switch in facing direction are analyzed. The main results indicate that eliminating alignment irregularities before the switch can effectively improve the dynamic performance of the integrated wheelset in the switch and the lateral forces of the outer wheels of these two vehicles are reduced by about 80%, the derailment coefficients are reduced by about 70%, the vertical force is reduced by about 10–20% and wheel load is reduced by approximately 30%.

Crack energy density of a piezoelectric material under general electromechanical loading

The problem of a circular plate, with a central hole, elastically constrained against rotation and deflection, acted upon by a transverse linear temperature gradient or a general axisymmetrical loading condition is considered in this paper. With the aid of presented graphs and simple algebraic equations, it is a relatively simple matter to construct the desired deflection and stress pattern for any combination of elastic constraints and load distribution.

New, exact nonlinear virtual work equations for plane frames are rigorously derived and applied to problems of ‘frames’, whose members maybe treated as inextensible, as opposed to ‘trusses’. The virtual work equations are used to establish a simple stability discriminant (non-negative for stability); to investigate the orthogonality and completeness properties of the sequences of eigenfunction displacement modes generated by arbitrary axial loading; and to discuss various features of the response to non-axial loading. The concept of the ‘ current critical load’, which determines the stability of the frame, is introduced, and certain principles governing bifurcation under non-axial loading are established. Two methods of computing the nonlinear equilibrium path of an arbitrary elastic frame under general loading are developed, and an example is given of the direct evaluation of the maximum load according to small displacement theory.

Railway vehicles will inevitably appear wheel diameter difference, which will result in an unsymmetrical contact of wheel and rail. Take the guide wheelset for example, analysed the influence of the wheel diameter difference on the wheelset loading state and movement patterns in detail. Based on it, the train model which make up of 2(B0–B0) axle type locomotives + C80 wagon were set up. The effect of wheel diameter difference on the dynamic wheel/rail contact relation under coasting condition as well as dynamic braking condition were analyzed. Simulation results show that the wheel diameter difference will change the wheel/rail dynamic contact relation and aggravate the wear of wheel/rail profile. The influence of wheel diameter difference in anti phase on the wheel/rail lateral force is bigger than that in same phase. Compare with coasting condition, the wheel/rail lateral force of smaller wheel will increase and the wheel/rail lateral force of bigger wheel will decrease under dynamic braking condition, the wheelset lateral force under dynamic braking condition is relatively smaller than coasting condition. Wheel diameter difference will cause the partial wear of wheelset under dynamic braking condition, and this will increase the wheel diameter difference further.

Furrow openers using single disc coulter operated at certain disc and tilt angles arebecoming common for single pass seeding operation. Concerns have been expressed as to theefficiency of disc to place seed and fertilizer at a proper depth, and resulting compaction of thefurrow wall. Tests were conducted in an indoor soil bin using 460 mm (18-in.), and 610 mm (24-in.)diameter disc coulters to determine the effect of combined disc and tilt angles on soil forces,and resulting furrow wall strength. Experiments were carried out using various levels ofcombined disc angles, moisture content, soil compaction, and depth of operations.Measurements were taken for draft, vertical force, side force, soil strength of the furrow wall,and furrow profile. Results indicated that the most favorable condition in terms of the lowestvalues of draft, vertical force, side force, and soil strength of the furrow wall were obtained with610 mm diameter disc at 5&15 combined angle. However, for 460 mm diameter disc, thelowest values of draft and side forces were obtained with 5&15 and 5&25 combined angles,respectively.

This paper presents new solutions of a three-dimensional (3D) interaction diagram for the undrained capacity of inverted T-shape strip footings under general loading. The two-dimensional plane strain finite-element analysis was employed to determine the stability of this problem. Parametric studies were performed to study the interactions of the combined vertical load (V), horizontal load (H) and bending moment (M) that were applied on top of the inverted T-shape footing. The combined action of vertical forces included both tensile (upward) and compressive (downward) loadings. The results of these analyses were summarised in terms of the dimensionless factors for V, H and M. Failure mechanisms associated with different locations on the 3D interaction diagram were compared and discussed. A closed-form approximate solution of the 3D interaction diagram for inverted T-shape strip footings under the V–H–M loading was proposed and compared with the finite-element solutions.

In the finite element modelling of structural frames, external loads such as wind loads, dead loads and imposed loads usually act along the elements rather than at the nodes only. Conventionally, when an element is subjected to these general transverse element loads, they are usually converted to nodal forces acting at the ends of the elements by either lumping or consistent load approaches. In addition, it is especially important for an element subjected to the first- and second-order elastic behaviour, to which the steel structure is critically prone to; in particular the thin-walled steel structures, when the stocky element section may be generally critical to the inelastic behaviour. In this sense, the accurate first- and second-order elastic displacement solutions of element load effect along an element is vitally crucial, but cannot be simulated using neither numerical nodal nor consistent load methods alone, as long as no equilibrium condition is enforced in the finite element formulation, which can inevitably impair the structural safety of the steel structure particularly. It can be therefore regarded as a unique element load method to account for the element load nonlinearly. If accurate displacement solution is targeted for simulating the first- and second-order elastic behaviour on an element on the basis of sophisticated non-linear element stiffness formulation, the numerous prescribed stiffness matrices must indispensably be used for the plethora of specific transverse element loading patterns encountered. In order to circumvent this shortcoming, the present paper proposes a numerical technique to include the transverse element loading in the non-linear stiffness formulation without numerous prescribed stiffness matrices, and which is able to predict structural responses involving the effect of first-order element loads as well as the second-order coupling effect between the transverse load and axial force in the element. This paper shows that the principle of superposition can be applied to derive the generalized stiffness formulation for element load effect, so that the form of the stiffness matrix remains unchanged with respect to the specific loading patterns, but with only the magnitude of the loading (element load coefficients) being needed to be adjusted in the stiffness formulation, and subsequently the non-linear effect on element loadings can be commensurate by updating the magnitude of element load coefficients through the non-linear solution procedures. In principle, the element loading distribution is converted into a single loading magnitude at mid-span in order to provide the initial perturbation for triggering the member bowing effect due to its transverse element loads. This approach in turn sacrifices the effect of element loading distribution except at mid-span. Therefore, it can be foreseen that the load-deflection behaviour may not be as accurate as those at mid-span, but its discrepancy is still trivial as proved. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. Moreover, another significance of this paper is placed on shifting the nodal response (system analysis) to both nodal and element response (sophisticated element formulation). For the conventional finite element method, such as the cubic element, all accurate solutions can be only found at node. It means no accurate and reliable structural safety can be ensured within an element, and as a result, it hinders the engineering applications. The results of the paper are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple frames.

Parametric features of an UIC60 rail at weld bottom crack in transverse direction under weld-wheel contact forces

Canal dike characterization by means of electrical resistivity, shear wave velocity and particle size data fusion

Chair-seat height affects the burden on the lower-limbs during sit-to-stand (STS) movement. Previous studies used the same height chair, attaching importance to practicability, but the difference in each subject's lower thigh length may relate to the burden on the lower-limbs. This study aimed to examine the influence of different lower thigh lengths on floor reaction force and lower-limb strength during an STS movement. Thirty young-adult male subjects participated in this study (age: 22.7+/-2.6 yr, height: 172.8+/-4.8 cm, body-mass: 66.3+/-5.2 kg). The subjects were divided into three groups (G1>42 cm, 42 cm > or =G2 > or =38 cm, 38 cm >G3) based on lower thigh length (G1: 44.1+/-2.5 cm, G2: 39.8+/-1.3 cm, G3: 34.3+/-2.1 cm). Namely, G1 was characterized by lower thigh length longer than 105% of 40 cm, G2 by 95-105% of lower thigh length and G3 by lower thigh length less than 95% of 40 cm, respectively. Subjects performed an STS movement twice from chairs at 40 cm-height and height adjusted by the lower thigh length of each subject. Vertical floor reaction force and electromyogram (EMG) on the rectus femoris and tibialis anterior muscles during an STS movement were measured to evaluate the force of knocking over and the burden on the lower-limbs. Fifteen parameters regarding floor reaction force (10) and EMG (5) were selected for analyses. Significant differences were found in floor reaction force at hip-syneresis (F1) and the impulse between hip-syneresis and appearance of the peak floor reaction force (F2). G1 was greater than G2 for the former, and G3 for the latter. Significant differences were found in active muscle mass of the tibialis anterior from the beginning of an STS movement to hip-syneresis (TE1) and peak active muscle level of the tibialis anterior (TE6). G1 was greater than G2 for the former, and G2 and G3 for the latter. It was suggested that when an STS movement is performed using a chair with the same height for each subject, the load imposed on the subject's leg at the time of an STS movement and the STS movement achievement strategy differed since chair seat height changes relatively by the difference in lower thigh length. Moreover, it is thought that the difference in these load conditions and movement strategies occurs when the chair seat height of a subject's lower thigh length is longer than 110%. When conducting the ability to achieve STS movement rating test, chair seat height considering each subject's lower thigh length may be needed.

Non-prismatic beams are widely employed in several engineering fields, e.g., wind turbines, rotor blades, aircraft wings, and arched bridges. While analytical solutions for variable cross-section beams are desirable, a model describing all stress components for beams with general variation of their cross-section under generalised loading remains an open and important problem to solve. To partly address this issue, we propose an analytical solution for stress recovery of untwisted, asymmetric, non-prismatic beams with smooth and continuous taper shape under general loading, considering plane stress conditions for isotropic materials undergoing small strains. The methodology follows Jourawski’s formulation, including the effect of asymmetric variable cross-section, with internal forces as known variables. We confirm the non-triviality of the stress field of non-prismatic beams, i.e., the dependency on all internal forces and beam geometry to shear and transverse stress distributions. As a particular novelty, the new formulation for transverse direct stress includes internal forces derivatives, resulting in greater accuracy than state-of-the-art models for distributed loading conditions. Also, closed-form solutions are introduced for non-prismatic and linearly tapered, generally asymmetric beams, both with rectangular cross-sections. For validation purposes, we consider three different practical beam models: a symmetric and an asymmetric, both linearly tapered, and an arched beam. The results, checked against commercial finite element analysis, show that the proposed model predicts the stress-field of non-prismatic beams under distributed loads with good levels of accuracy. Traction-free boundary condition requirements are naturally satisfied on the beam surfaces.

Model tests on anomalous low friction and pendulum-type wave phenomena

Chapter 6.2 Ocean transport of fresh water