Numerical solution to the buckling problem for a sandwich plate under uniaxial compression

A thin rectangular sandwich plate with isotropic linear elastic layers is considered. The plate is in a plane-strain state under uniaxial compression. An exact statement of the buckling problem is given. Its approximate solution is found by the finite-difference method. The concept of base scheme is used to formulate discrete problems in explicit and compact form. As an example, the critical parameters of the plate are calculated using a computation optimization procedure. Its efficiency is demonstrated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 98–105, September 2006.     

正交各向异性加筋板屈曲分析方法研究

为简化正交各向异性加筋板屈曲分析,本文将筋条位移场用其所在位置的板的位移表达,建立加筋板总势能,通过离散位移场,利用最小势能原理,推导出基于里兹法的正交各向异性加筋板屈曲分析控制方程,采用Matlab进行求解.基于本文推导的方程对单筋和三筋加筋板在不同压剪比下的屈曲荷载和模态进行分析,得到与Abaqus基本一致的结果....     

Calibration of constitutive models of steel beams subject to local buckling by using digital image correlation

It is proposed to identify the behavior of steel beams prior to and after the inception of local buckling by using digital image correlation. Full-field measurements are used to evaluate kinematic and static fields for determining constitutive laws. It enables for the detection of local buckling inception and the evaluation of the post-buckled behavior. Constitutive models are tuned by using measured Euler–Bernoulli kinematics.     

On the influence of singular-type finite elements on the critical force in studying the buckling of a circular plate with a crack

The axisymmetric buckling (delamination) of a circular disk (plate) with a penny-shaped crack is analyzed using a continuum model, piecewise-homogeneous model, and the three-dimensional linearized theory of stability. The FEM is used. The analysis is carried out using various singular and ordinary finite elements. The numerical results obtained indicate that it is not necessary to use singular finite elements to solve the problem Published in Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 120–129, September 2007.     

A method for the estimation of plastic buckling loads

Certain elastic-plastic buckling problems require the solution of an appropriate incremental or “rate” boundary-value problem in order that physically meaningful results may be obtained. In this paper, it is shown that a recent general variational theorem by Neale[8] may be advantageous for the approximate solution of such problems. As an example, the buckling of elastic-plastic cylindrical shells under torsion is analyzed, wherein the material is assumed to obey the incremental theory of plasticity and the effects of initial imperfections in geometry are taken into account.     

On the applicability of the Southwell plot to plastic buckling

A completely forgotten paper by C.T. Wang on the extension of the Southwell plot to inelastic buckling of columns is revived, rederived and amplified. A theoretical justification is presented for the application of the Southwell method to plastic buckling of columns made of a strain-hardening material, showing that it predicts the double (or reduced) modulus buckling load. Typical experimental verifications are recapitulated. This puts practical applications of the Southwell method in the plastic region on firmer ground.     

Numerical implementation of a thermo-elastic–plastic constitutive equation in consideration of transformation plasticity in welding

Finite element analysis of welding processes, which entail phase evolution, heat transfer and deformations, is considered in this paper. Attention focuses on numerical implementation of the thermo-elastic–plastic constitutive equation proposed by Leblond et al. [J. Mech. Phys. Solids 34(4) (1986a) 395; J. Mech. Phys. Solids 34(4) (1986b) 411] in consideration of the transformation plasticity. Based upon the multiplicative decomposition of deformation gradient, hyperelastoplastic formulation is borrowed for efficient numerical implementation, and the algorithmic consistent moduli for elastic–plastic deformations including transformation plasticity are obtained in the closed form. The convergence behavior of the present implementation is demonstrated via a couple of numerical examples.     

Strain path theory of plastic constitutive relation

Based on Illiushin's two hypotheses, a new plastic constitutive equation of integral type is proposed. The deviatoric stress induced by a strain path consists of two parts which vary according to different laws. Comparison of theoretical calculation with recent experiments is satisfactory. The present theory is not an endochronic theory.     

Studies on the dynamic buckling of circular plate irradiated by laser beam

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Numerical simulation of viscoelastic flows with Oldroyd-B constitutive equations and novel algebraic stress models

The purpose of the present study is to compare numerical simulations of viscoelastic flows using the differential Oldroyd-B constitutive equations and two newly devised simplified algebraic explicit stress models (AES-models). The flows of a viscoelastic fluid in a 180° bent planar channel and in a 4:1 planar contraction are considered to illustrate and support the underlying theory. The flow in the bent channel is used to illustrate the frame-invariant property of the new models in a pure shear flow exhibiting strong streamline curvature. The flow in the 4:1 contraction serves as a benchmark test in a situation where strong elongation occurs. For both geometries, it is found that the predictions of the new AES-models are in good agreement with Oldroyd-B up to Deborah numbers of order 0.5, with a significant reduction in computational effort.     

Numerical study on flanging and spring-back of stamped thick metal plate

A quasi-three-dimensional shell element model, which can be effectively used to simulate the flanging and spring-back deformation, is introduced into the independently developed CAE software, KMAS. In this model, a double surface contact algorithm, which allows the gap between punch and die to change, and a spring-back treatment scheme based on finite element meshing are described. And then the flanging and spring-back deformations of the retractor's kickstand of a railcar made of stamped thick metal plate are numerically simulated. The simulation results of flanging deformation are compared with those of international commercial software, PAM-STAMP, and experimental ones. Finally, a predicting scheme of spring-back quantily for this problem is given. Project supported by the National Natural Science Foundation of China (No. 19832020) and the Ministry of Education of China.     

On the problems of buckling of an annular thin plate

In this paper, problems of buckling of an annular thin plate under the action of in-plane pressure and transverse load are studied by using the method of multiple scales. We obtain N-order uniformly valid asymptotic expansion of the solution. In the latter part of this paper we discuss a particular example, and calculate the critical value of in-plane pressure. We see that the asymptotic expansion obtained by the multiple scales is completely consistent with that of the exact solution.     

A numerical study of constitutive models endowed with Pom-Pom molecular attributes

The branched polymer melts are modeled respectively in this investigation by the existing XPP and PTT–XPP models, along with the proposed S-MDCPP (Single/Simplified Modified Double Convected Pom-Pom) model developed on the basis of the existing MDCPP model. A pressure stabilized mass equation is formulated with the finite increment calculus (FIC) process to restrain and further eliminate spurious oscillations of pressure field due to the incompressibility of fluids. The discrete elastic viscous stress splitting (DEVSS) technique is employed, in order to retain an elliptic contribution in the weak form of the momentum equation. An inconsistent streamline-upwind (SU) method is applied to spatially discretize the constitutive equations. The mass, momentum conservation and constitutive equations are discretized and solved by the iterative stabilized fractional step algorithm along with the Crank–Nicolson implicit difference scheme. Thus the finite elements with equal low-order interpolation approximations for velocity–pressure–stress variables can be devised to numerically simulate the viscoelastic contraction flows for branched LDPE melts. The influences of the three viscoelastic constitutive models and the branched arms at the end of the Pom-Pom molecule on the rheological behaviors occurring in this complex flow are discussed. The numerical results demonstrate that the proposed S-MDCPP model is capable of reproducing some properties similar to those predicted by the XPP model in high shear flow and, on the other hand, reproducing some properties similar to those predicted by the PTT–XPP model in high elongational flow. Furthermore, the proposed S-MDCPP model is capable of well identifying the macromolecule topological structures of branched polymer melts.     

The impact torsional buckling for the rigid plastic cylindrical shell

By using the energy criterion in[3],the impact torsional buckling for the rigid plastic cylindrical shell is studied.The linear dynamic torsional buckling equations for the rigid plastic shell is drived,and the critical impact velocity is given.     

Numerical study of the natural convective cooling of a vertical plate

We study numerically in this paper the natural convective cooling of a vertical plate. The full transient heat conduction equation for the plate, coupled with the natural convection boundary layer equations are solved numerically for a wide range of the parametric space. Assuming a large Rayleigh number for the natural convection flow, the balance equations are reduced to a system of three differential equations with three parameters: the Prandtl number of the fluid, Pr, a non-dimensional plate thermal conductivity α and the aspect ratio of the plate ?. The nondimensional cooling time depends mainly on α/?², obtaining a minimum of this time for values of 1?α??².     

Dynamic elastic and plastic buckling of complete spherical shells

A theoretical investigation is undertaken into the dynamic instability of complete spherical shells which are loaded impulsively and made from either linear elastic or elastic-plastic materials. It is shown that certain harmonics grow quickly and cause a shell to exhibit a wrinkled shape which is characterized by a critical mode number. The critical mode numbers are similar for spherical and cylindrical elastic shells having the same R/h ratios and material parameters, but may be larger or smaller in an elastic-plastic spherical shell depending on the values of the various parameters. Threshold velocities are also determined in order to obtain the smallest velocity that a shell can tolerate without excessive deformation. The threshold velocities for the elastic and elastic-plastic spherical shells are larger than those which have been published previously for cylindrical shells having the same R/h ratios and material parameters.     

On modes of buckling for a plate on an elastic foundation

We study flexural stability of a homogeneous plate compressed in its plane and lying on an elastic foundation. There is an elastic stratum between the plate and the foundation. In the case of homogeneous uniform compression, the linear approximation does not answer the question of the shape of buckling. A geometrically nonlinear approach leads to the conclusion that the buckling shape is of staggered character.     

Flow effects of blood constitutive equations in 3D models of vascular anomalies

The effects of different blood rheological models are investigated numerically utilizing two three‐ dimensional (3D) models of vascular anomalies, namely a stenosis and an abdominal aortic aneurysm model. The employed CFD code incorporates the SIMPLE scheme in conjunction with the finite‐volume method with collocated arrangement of variables. The approximation of the convection terms is carried out using the QUICK differencing scheme, whereas the code enables also multi‐block computations, which are useful in order to cope with the two‐block grid structure of the current computational domain. Three non‐Newtonian models are employed, namely the Casson, Power‐Law and Quemada models, which have been introduced in the past for modelling the rheological behaviour of blood and cover both the viscous as well as the two‐phase character of blood. In view of the haemodynamical mechanisms related to abnormalities in the vascular network and the role of the wall shear stress in initiating and further developing of arterial diseases, the present study focuses on the 3D flow field and in particular on the distribution as well as on both low and high values of the wall shear stress in the vicinity of the anomaly. Finally, a comparison is made between the effects of each rheological model on the aforementioned parameters. Results show marked differences between simulating blood as Newtonian and non‐Newtonian fluid and furthermore the Power‐Law model exhibits different behaviour in all cases compared to the other models whereas Quemada and Casson models exhibit similar behaviour in the case of the stenosis but different behaviour in the case of the aneurysm. Copyright © 2005 John Wiley & Sons, Ltd.