材料和几何线性的有限条分析

本文建立了大挠度弹塑性有限条法,用以计算初曲板在面内荷载作用下的极限荷载。分析中采用了伴随修正的Ilyushin屈服准则或修正的Ivanov屈服准则和Prandtl—Reuss塑性流动法则的面积法。通过与前人对板屈曲后弹塑性分析算例的比较,证明该方法对于板的大挠度弹塑性分析具有相当高的精度。     

Transverse Distributions of Front and Back Tension Stresses in Cold Strip Rolling

In this paper,such a new lateral displacement function is proposed that the lateral flow velocity is con-tinuous at the entry and the exit of deformation zone.A new kind of finite strip method—the third powerB-spline finite strip method—is put forward to simulate strip rolling process.Front and back tension stressesare formulated.The computed results of the transverse distributions of the front and back tension stresses areclose to the experimental results.The paper lays a foundation for further analysing the three-dimensionalstresses and deformations of strip rolling.     

On the dynamic propagation of an anti-plane shear crack in a functionally graded piezoelectric strip

Summary. In this paper, a finite crack propagating at constant speed in a functionally graded piezoelectric material (FGPM) is studied. It is assumed that the electroelastic material properties of the FGPM vary continuously according to exponential gradients along the thickness of the strip, and that the strip is under anti-plane shear mechanical and in-plane electrical loads. The analysis is conducted on the electrically unified (natural) crack boundary condition, which is related to the ellipsoidal crack parameters. By using the Fourier transform, the problem is reduced to the solutions of Fredholm integral equations of the second kind. Numerical results for the stress intensity factor and crack sliding displacement are presented to show the influences of the elliptic crack parameters, crack propagation speed, electric field, FGPM gradation, crack length, and electromechanical coupling coefficient. It reveals that there are considerable differences between traditional electric crack models and the present unified crack model.     

Dynamic response of strip footings on elastic halfspace

Dynamic response of strip footings resting on a soil medium, idealized as an elastic halfspace, is obtained using the finite element discretization technique with constant strain rectangular elements consisting of 4CST elements. Boundary stresses have been computed using a combination of Rayleigh wave absorbing boundaries (RAB) and standard vicous boundaries (SVB). The influences of contact pressure distributions at the footing—soil interface, mass and frequency ratios on the dynamic response of a strip footing are studied. Effects of embedment, static surcharge, nonhomogeneity and nonlinear constitutive relations are shown. Results are compared with the existing solution and are presented graphically.     

Eddy currents in a transverse MRI gradient coil

A transverse gradient coil (x- or y-coil) of an MRI-scanner is modeled as a network of curved circular strips placed at the surface of a cylinder. The current in this network is driven by a time-harmonic source current. The low frequency applied allows for an electro-quasi-static approach. The strips are thin and the current is assumed to be uniformly distributed in the thickness direction. For the current distribution in the width direction of the strips, an integral equation is derived. Its logarithmically singular kernel represents inductive effects related to the occurrence of eddy currents. For curved circular strips of width much smaller than the radius of the cylinder one may locally replace the curved circular strip by a tangent plane circular strip. This plane geometry preserves the main characteristics of the transverse current distribution through the strips. The current distribution depends strongly on the in-plane curvature of the strips. The Petrov–Galerkin method, using Legendre polynomials, is applied to solve the integral equation and shows fast convergence. Explicit results are presented for two examples: a set of 1 strip and one of 10 strips. The results show that the current distributions are concentrated near the inner edges and that resulting edge-effects, both local and global, are non-symmetric. This behavior is more apparent for higher frequencies and larger in-plane curvatures. Results have been verified by comparison with finite-element results.     

Semi-analytical model based on generalized plane strain assumption for unidirectional composites with matrix micro cracks

Generalized plane strain state is assumed and stress-based finite strip method is formulated for analysis of unidirectional laminates with matrix microcracks. Total complementary potential energy is minimized and fourth-order Euler Lagrange governing equations are presented. This stress-based generalized plane strain approach analyzes general layup and loading conditions. It provides flexibility to control the number of finite strip nodal lines within each lamina; hence, stress behavior can be predicted across each lamina at the desired location of the structure. Along with all of the capabilities which are common with finite strip methodology based on plane strain assumption, this current work has extended the analysis of the cracked laminate. For example, by incorporating behavior of the out of the plane shear stress, boundary conditions including natural boundary conditions are imposed appropriately to solve governing Euler's equations. Results are compared with previously developed displacement-based formulation in the literature for cracked laminates. It has already been shown that a stress-based plane strain approach enhances variation-based cracked laminate analysis where only the case of cross-ply laminate under tension is considered. This current work applies generalized plane strain-based finite strip methodology to carry out analysis under different loading conditions.     

An improved ‘assumed enhanced displacement gradient’ ring‐element for finite deformation axisymmetric and torsional problems

Analyzing axisymmetric solids under torsional loading the 3d(imensional) problem can always be reduced by one dimension, since the displacement field and the rotation field are independent of the cylindrical (angle) co‐ordinate Θ, respectively. For this purpose a four‐node ring‐element for finite deformation axisymmetric and torsional problems was recently developed and is now going to be up‐dated. The original assumption of the enhanced displacement gradient H̃ = α _i⊗ G ⁱ is expanded in two steps according to Simo, Armero and Taylor and to Glaser and Armero, respectively: firstly in defining the additional unknowns (parameters) α _i as objects in the material configuration and pushing forward H̃ by ( 1 + U ⊗ Grad ) ∣ξ=0—this provides ‘objectivity’—and secondly in replacing α _i⊗ G ⁱ by G _i⊗ α ⁱ. Numerical results of three classical benchmarks, the in‐plane torsion test, the copper rod impact and the thermomechanical localization of a rectangular strip are presented. Copyright © 2001 John Wiley & Sons, Ltd.     

THE p-VERSION OF THE FINITE ELEMENT METHOD IN INCREMENTAL ELASTO-PLASTIC ANALYSIS

Whereas the higher-order versions of the finite element method (p- and hp-versions) are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems, little has been done to exploit their benefits in elasto-plastic structural analysis. In this paper, we discuss which aspects of incremental elasto-plastic finite element analysis are particularly amenable to improvements by the p-version. These theoretical considerations are supported by several numerical experiments. First, we study an example for which an analytical solution is available. It is demonstrated that the p-version performs very well even in cycles of elasto-plastic loading and unloading, not only as compared with the traditional h-version but also with respect to the exact solution. Finally, an example of considerable practical importance—the analysis of a cold-working lug—is presented which demonstrates how the modelling tools offered by higher-order finite element techniques can contribute to an improved approximation of practical problems.     

An investigation on the post-buckling behavior of symmetric cross-ply laminated plates using a semi-energy finite strip approach

A geometrically non-linear finite strip for the post-buckling analysis of geometrically perfect thin symmetric cross-ply laminated plates under uniform end shortening is presented in this paper. The formulation of the aforementioned finite strip is based on the concept of the semi-energy approach. In this method, the out-of-plane displacement of the finite strip is the only displacement which is postulated by a deflected form. The postulated deflected form is substituted into von Kármán’s compatibility equation which is solved exactly to obtain the corresponding forms of the mid-plane stresses and displacements. The solution of von Kármán’s compatibility equation and the postulated out-of-plane deflected form are then used to evaluate the potential energy of the related finite strip. Finally, by invoking the Principle of Minimum Potential Energy, the equilibrium equations of the finite strip are derived. The developed finite strip is then applied to analyze the post-local-buckling behavior of thin flat laminates. The results are discussed in detail and compared with those obtained from finite element method (FEM) of analysis. It should be mentioned that the FEM analysis was carried out employing the general purpose ANSYS package. The study of the results has provided confidence in the validity and capability of the developed finite strip in handling the post-buckling problem of symmetric cross-ply laminated plates.     

Analytical solutions of fully plastic crack-tip higher order fields under antiplane shear

Analytical solutions of higher order fields in a fully plastic power-law hardening material are presented. By the use of hodograph transformation and asymptotic analysis the stress and strain exponents, angular distributions of shear stresses and strains are analytically determined. Special cases, such as linearly elastic, perfectly plastic materials are discussed. Similar characteristics between mode III and mode I plane strain, and mode II plane stress are examined. Comparison of four-term asymptotic solutions with exact and leading term solutions in an infinite strip with a semi-infinite crack under constant displacements along its edges is provided.     

Numerical study of geometric constraint and cohesive parameters in steady-state viscoelastic crack growth

This paper presents a finite element study of cohesive crack growth in a thin infinite viscoelastic strip to investigate the effects of viscoelastic properties, strip height, and cohesive model parameters on the crack growth resistance. The results of the study show that the dependence of the fracture energy on the viscoelastic properties for the strip problem is similar to that obtained for the infinite body problem even when the cohesive zone length is large compared to the height of the strip. The fracture energy also depends on the crack speed v through the dimensionless parameter v τ/L _∞ where L _∞ is the characteristic length of the cohesive zone and τ is the characteristic relaxation time of the bulk material. This relationship confirms that at least two properties of the fracture process must be prescribed accurately to model viscoelastic crack growth. In contrast, the fracture energy and crack speed are insensitive to the strip height even in situations where the growth of the dissipation zone is severely constrained by the strip boundaries. We observe that at high speeds, where the fracture energy asymptotically approaches the maximum value, the material surrounding the cohesive zone is in the rubbery (equilibrium) state and not the glassy state.     

Dynamic problem of expanding crack under concentrated load

An analysis is presented on a dynamic problem of two-dimensional crack which is subjected to a time-increasing concentrated load on the surface and expands at both ends at a constant velocity. The dynamic stress intensity factor and the dynamic energy release rate are calculated for a linear elastic solid. A further extension of elastic analysis with simulated plasticity is made by the strip yield model, the Dugdale's model. It is shown that the plastic zone length, the COD and the energy release rate are expressed by functions decreasing with the crack velocity.     

Buckling analysis of composite laminates under end shortening by higher‐order shear deformable finite strips

A higher‐order shear deformable finite strip is developed and employed in the buckling analysis of laminated composite plates when subjected to uniform end shortening. This enables the transverse shear deformation to be accurately incorporated. The permitted laminate material properties are quite general, encompassing anisotropy and full coupling between in‐plane and out‐of‐plane behaviour. Results with respect to the number of plies, thickness of laminate and ratios of E₁₁/E₂₂ are presented for unsymmetric cross‐ply and angle‐ply lay‐ups and for laminates with arbitrary lay‐up arrangements. Copyright © 2002 John Wiley & Sons, Ltd.     

Mathematical modelling of an experimental‐analytical method for friction coefficient determination in deep drawing

The main aim of this paper is to determine the friction coefficient μ and maximum drawing force in deep drawing process of aluminum alloy EN AW 1050 utilizing strip drawing method. Influence and interaction between lubrication condition, blank holder force and strip surface roughness on maximum drawing force and friction coefficient are investigated. Response surface methodology and D‐Optimal design are utilized in order to create an experimental plan. According to the design, 23 strip drawings experiments are performed and statistical analysis was done. The regression and variance analysis results with 18 significant mathematical models which are derived in order to describe influence of mentioned parameters on friction coefficient and maximum drawing force. Results are discussed according to previous research. Finally, the optimization of processing parameters is performed aiming for lower friction coefficient and maximal drawing force.     

An anisotropic strip weakened by an array of cracks

The paper deals with a 2-dimensional problem of an anisotropic elastic strip having an infinite row of Griffith cracks. By using integral equation approach, the problem is treated analytically. The stress intensity factor, the critical pressure and the energy required to open the crack are studied for two cases—(a) when the edges of the strip are in contact with smooth and rigid planes and (b) when the edges of the strip are free of tractions. Numerical results for the aforementioned quantities are obtained for both the cases for a specific anisotropic material and a comparison is made with the corresponding results for a strip made of an isotropic material.     

Stress and failure analysis of laminated composites based on layerwise B-spline finite strip method

A layerwise B_k,k−1-spline finite strip method is developed for stress and failure analysis in fibre reinforced composite laminates. The composite laminates are divided into a number of numerical layers in the thickness direction. A linear variation of in-plane displacements are assumed across the thickness of each numerical layer to represent the sectional warping which can have significant effects on through thickness shear stresses. The development of B_k,k−1-spline finite strip method is presented. Material failure criteria and material degradation models for progressive failure are discussed and integrated in a progressive failure analysis for composite laminates. Numerical applications include a progressive failure analysis example are presented to verify the layerwise B-spline finite strip method developed for stress and failure analysis in composite laminates. Whenever possible the present predictions are compared with the existing analytical and numerical results.     

Free vibration analysis and shape optimization of prismatic folded plates and shells with circular curved planform

This paper deals with the elastic free vibration analysis and structural shape optimization of prismatic folded plate and shell structures with circular curved planform. The structures are supported on diaphragms at two opposite edges. The basic formulation of a family of curved variable thickness C(0) Mindlin–Reissner finite strips is presented. The accuracy and performance of these newly developed strips are explored through a series of examples including annular plate sectors, a box girder bridge and a cylinder with an interior longitudinal plate. Numerical results obtained are compared with results from other sources. The whole shape optimization process is carried out by integrating finite strip analysis, cubic spline shape and thickness definition, sensitivity analysis and mathematical programming. The objective is either the maximization of the fundamental frequency or the minimization of volume by changing the shape or thickness variation of the cross-section of the structure with constraints on the volume or natural frequencies. Several examples are included to illustrate and highlight various features of the optimization, including annular sector plates, a curved box girder bridge and a cylinder shell segment with curved pianform.     

Antiplane shear analysis of a semi-infinite multi-layered monoclinic strip

Summary Elasticity solutions for a semi-infinite multi-layered monoclinic strip subject to antiplane shear deformation are presented. The solutions are obtained by the method of eigenfunction expansion in conjunction with Betti's reciprocity theorem. In particular, a compact closed-form solution for a two-layered strip loaded by a uniform shear stress at the end is obtained. The solution for the two-layered strip shows that at the interface the traction possesses a logarithmic singularity at the loaded end.     

Instabilities of Regression Estimates Relating Air Pollution to Mortality

The instability of ordinary least squares estimates of linear regression coefficients is demonstrated for mortality rates regressed around various socioeconomic, weather and pollution variables. A ridge regression technique presented by Hoer1 and Kennard (Technometrics 12 (1970) 69–82) is employed to arrive at “stable” regression coefficients which, in some instances, differ considerably from the ordinary least squares estimates. In addition, two methods of variable elimination are compared—one based on total squared error and the other on a ridge trace analysis.