Limit Design in the Absense of a Given Layout: A Finite Element,Zero-One Programming Approach∗

Limit design in three dimensions is discussed and formulated as a constrained minimax problem in kinematic and geometric variables. A finite element discretization is proposed which, combined with piecewise linearization of the yield surfaces, reduces the minimum weight design to a pair of dual problems in linear mixed zero one programming. The relevant duality theory is shown to be useful for the theoretical frame of the mechanical problem. Various ways of reducing the number of variables and constraints are pointed out, in order to make available algorithms economically applicable to practical situations.     

Rigid Plastic Plates under a Concentrated Moving Load∗

A rigid-plastic rectangular plate subjected to a moving transverse load is analyzed. The load is too large for the plate to be supported under static conditions. The present study indicates that there is a critical value for the moving load, above which the crossing cannot be made, irrespective of its speed. The relation between the moving load and its speed is given for values less than ciritical, as well as the distribution of displacement for a simply supported rectangular plate.     

The Motion of a Fluid–Rigid Disc System at the Zero Limit of the Rigid Disc Radius

We consider the two-dimensional motion of the coupled system of a viscous incompressible fluid and a rigid disc moving with the fluid, in the whole plane. The fluid motion is described by the Navier–Stokes equations and the motion of the rigid body by conservation laws of linear and angular momentum. We show that, assuming that the rigid disc is not allowed to rotate, as the radius of the disc goes to zero, the solution of this system converges, in an appropriate sense, to the solution of the Navier–Stokes equations describing the motion of only fluid in the whole plane. We also prove that the trajectory of the centre of the disc, at the zero limit of its radius, coincides with a fluid particle trajectory.     

‘Velocity’Finite Element Method for Dynamic Problem

After analysing the essential features of successive integration method taking displacementas variable by N.M.Newmark and E.L.Wilson et al,this paper presents a“Velocity”Element Method,taking velocity as variable for the solution of the initial value problem.A simplified scheme is offered for the non-damping system,and the stability is also discussed.Owing to the fact that this simplified scheme for non-damping and apparent static damping is explicitin form,it is unnecessary to solve the algebraic system of equations at every time interval,conse-quently the amount of computation is greatly reduced.For non-linear dynamic problems,this schememay be used to obtain fairly good initial values for iteration.An extended form of“elocity”Element is presented for the arbitrary damping system.For thenon-linear cases,the incremental Velocity iteration scheme is adopted and its convergence proved.Some discussions have been given on artificial damping and the effect of the parameter.Finally,the results of numeric     

A New Stable Bubble Element for Incompressible Fluid Flow Based on a Mixed Petrov–Galerkin Finite Element Formulation

A new mixed Petrov–Galerkin formulation employing the MINI element with a non-confirming bubble function for an incompressible media governed by the Stokes equations, which is equivalent to the stabilized finite element by P ¹-P ¹ approximation, is proposed. The new formulation possesses better stability properties than the conventional Bubnov–Galerkin formulation employing the MINI element. In this aspect, the stabilizing effect of this formulation is evaluated by a stabilizing parameter determined by both shapes of the trial and the weighting bubble functions.     

DISCUSSIONS On "Finite Element Analysis of Axisymmetric Elastic Body Problems

Regarding the calculdtion of the rigidity matrix of the linear triangular elements, there is really the existence of the nonconvergent terms. But the corresponding rows and columns of these terms     

Finite Element Analysis of Cauchy–Born Approximations to Atomistic Models

This paper is devoted to a new finite element consistency analysis of Cauchy–Born approximations to atomistic models of crystalline materials in two and three space dimensions. Through this approach new “atomistic Cauchy–Born” models are introduced and analyzed. These intermediate models can be seen as first level atomistic/quasicontinuum approximations in the sense that they involve only short-range interactions. The analysis and the models developed herein are expected to be useful in the design of coupled atomistic/continuum methods in more than one dimension. Taking full advantage of the symmetries of the atomistic lattice, we show that the consistency error of the models considered both in energies and in dual W ^1,p type norms is ${\mathcal{O}(\varepsilon^2)}$ , where ${\varepsilon}$ denotes the interatomic distance in the lattice.     

On the Buckling of an Infinite Beam of Finite Width Embedded in an Isotropic Elastic Solid∗

The present paper considers the problem of buckling of a beam of finite width that is embedded in bonded contact with an isotropic elastic solid. Analysis of the buckling problem is restricted to the class of slender beams of narrow width that exhibit flexure only in the longitudinal direction. The governing integral equations are solved in an approximate fashion. Numerical results presented indicate the manner in which the buckling load is influenced by the relative flexibility of the beam-elastic medium system.     

Plastic Stress Distribution in a Rotating Disk with Rigid Inclusion Under a Radial Temperature Gradient∗

Abstract

This study investigates the plastic stress distribution in a rotating disk with rigid inclusion, under an axially symmetric steady-state temperature gradient. The analysis is based on Tresca's yield condition, its associated flow rule, and linear strain hardening material behavior.

     

The Fundamental Equations in Finite Element Method of Coupled Thermo-elastic Plane Problem

The fundamental equations in finite element method for unsteady temperature field elasticplane problem are derived on the bases of variational principle of coupled thermoelastic problems.In these derivations,elastic plane is divided into three nodes triangular elements,and time interval isdivided into linear time elements,in which all the variables,including displacements and temperaturesat various nodal points,are varied linearly with time.Two coupled sets of linear algebraic equations ofall the unknown displacements and temperatures at every nodal point in every instant(i.e.the terminalvalues of time elements)are obtained.They are the fundamental equations of the said problem.     

The Solution for Axisymmetrical Shells with Abrupt Curvature Change(Corrugated Shells)by the Finite Element Method

It has been noted in the present paper that the finite element method using linear elements for solving axisymmetrical shells cannot be applied to the analysis of axisymmetrical shells with abrupt curvature change,owing to the fact that the influence of the curvature upon the angular displace-ments has been neglected.The present paper provides a finite element method using linear elements in which the influence of curvature is considered and the angular displacements are treated as continuous parameters.This method has been applied to the calculation of corrugated shells of the type C,and compared with the experimental results obtained by Turner-Ford as well as with the analytical solution given by Prof.Chien Wei-zang.The compari-sons have been proved that this theory is correct.     

An Experimental–Numerical Methodology for a Rapid Prototyped Application Combined with Finite Element Models in Vertebral Trabecular Bone

In the present study, a novel evaluation method involving rapid prototyped (RP) technology and finite element (FE) analysis was used to study the elastic mechanical characteristics of human vertebral trabecular bone. Three-dimensional (3D) geometries of the RP and FE models were obtained from the central area of vertebral bones of female cadavers, age 70 and 85. RP and FE models were generated from the same high-resolution micro-computed tomography (μCT) scan data. We utilized RP technology along with FE analysis based on μCT for high-resolution vertebral trabecular bone specimens. RP models were used to fabricate complex 3D objects of vertebral trabecular bone that were created in a fused deposition modeling machine. RP models of vertebral trabecular bone are advantageous, particularly considering the repetition, risks, and ethical issues involved in using real bone from cadaveric specimens. A cubic specimen with a side length of 6.5 mm or a cylindrical specimen with a 7 mm diameter and 5 mm length proved better than a universal cubic specimen with a side length of 4 mm for the evaluation of elastic mechanical characteristics of vertebral trabecular bones through experimental and simulated compression tests. The results from the experimental compression tests of RP models closely matched those predicted by the FE models, and thus provided substantive corroboration of all three approaches (experimental tests using RP models and simulated tests using FE models with ABS and trabecular bone material properties). The RP technique combined with FE analysis has potential for widespread biomechanical use, such as the fabrication of dummy human skeleton systems for the investigation of elastic mechanical characteristics of various bones.     

On the “Best” Mode Form in the Mode Approximation Technique Using the Finite Element Method

A systematic procedure for choosing the “best” mode shape is discussed by extending the mode approximation technique. The finite element method is used to calculate several valid mode forms of a given structure. Nonlinear eigenvalue problems are solved by an iterative procedure in order to obtain mode forms. Since one can choose only one mode form in the mode approximation technique due to nonlinearity of viscoplastic materials, the lower bound theorem on final time is applied to identify the best mode form. The validity of the concept is demonstrated by numerical results from two example problems of clamped beam and portal frame.     

Accuracy Analysis of the Semi-Analytical Method for Shape Sensitivity Calculation∗

ABSTRACT

The semi-analytical method of design sensitivity analysis that is widely used for calculating derivatives of static response with respect to design variables for structures modeled by finite elements is studied in this paper. It is shown that the method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. Errors are shown to be associated with an incompatibility of the sensitivity field with the structure. An error index is developed to test the accuracy of the semi-analytical method. It characterizes the difference in errors between a general finite difference method and the semi-analytical method. A method for improving the accuracy of the semi-analytical method (when possible) is provided. Examples are presented to demonstrate the use of the error index.     

On a Theory of the Infusion Method of Measuring the “Opening Pressure” in the Urethra

At rest the muscles which control the urethra (urine duct) are contracted and its lumen is practically equal to zero over its entire length. To open the urethra, a mechanical effort (due, for example, to a pressure rise in the bladder) must be applied. Reduced contractile activity of the muscles may be one of the reasons for incontinence (enuresis). A widespread method of estimating the blocking capability of the urethra consists in inserting a catheter with lateral perforations near the end. The catheter enters the bladder and is then removed at a constant velocity while a fluid is constantly pumped (infused) into it by a syringe pump at a steady rate and then flows out through the gap between the catheter and the urethral wall. The pumping pressure is considered to be a local measure of the blocking capability, and its dependence on the location of the catheter is regarded as an important diagnostic characteristic.Below, we will consider the simple, longitudinally homogeneous model system formed by an elastic tube pulled over a catheter segment when the initial stresses in the tube are constant over its length. An incompressible viscous fluid flows out of the perforations and percolates in a thin layer along the catheter. In solving the model problem, we will use the lubricating layer approximation under the assumption of small layer curvature. On the basis of an analysis of the results and a comparison of the model with a practical intraurethral measurement procedure, we discuss, firstly, the relationship between the measured quantities and the real characteristics of the urethra and, secondly, the possible formulation of a more realistic model problem.     

Justification of the Nonlinear Schrödinger Equation for the Evolution of Gravity Driven 2D Surface Water Waves in a Canal of Finite Depth

In 1968 V.E. Zakharov derived the Nonlinear Schrödinger equation for the two-dimensional water wave problem in the absence of surface tension, that is, for the evolution of gravity driven surface water waves, in order to describe slow temporal and spatial modulations of a spatially and temporarily oscillating wave packet. In this paper we give a rigorous proof that the wave packets in the two-dimensional water wave problem in a canal of finite depth can be approximated over a physically relevant timespan by solutions of the Nonlinear Schrödinger equation.     

Exact Solution of the Wave‐Resistance Problem for a Submerged Cylinder. I. Linearized Theory

. We consider the problem of finding a holomorphic function in a strip with a cut ${\cal A}= \{(x,y) : \, x\in\RE,\,\,0 satisfying some prescribed linear conditions on the boundary. The problem has a one‐parameter family of solutions in the class of sectionally holomorphic functions in ?, vanishing for $|x|\to\infty. We consider the problem of finding a holomorphic function in a strip with a cut satisfying some prescribed linear conditions on the boundary. The problem has a one‐parameter family of solutions in the class of sectionally holomorphic functions in ?, vanishing for . A special solution can be selected by fixing the value of the circulation around the cut. The problem is obtained by linearization of the equations of the wave‐resistance problem for a “slender” cylinder submerged in a heavy fluid and moving at uniform speed in the direction orthogonal to its generators. The results obtained, besides their own interest, are a crucial step for the resolution of the non‐linear problem. (Accepted October 14, 1998)     

Derivation of the LSW‐Theory for Ostwald Ripening by Homogenization Methods

. The coarsening of a solid phase in an undercooled liquid is described by a Stefan problem with surface tension. The solid phase is characterized by a large number of balls with small volume fraction and small capacity. We solve the quasi‐static equation as well as the parabolic problem and construct approximate solutions by means of comparison principles. The framework of Young measures is used to pass to the limit of infinitely many particles. We obtain that the capacity is the crucial quantity to get the conservation law for the particle size distribution which is studied in the classical theory for Ostwald ripening by Lifshitz, Slyozov & Wagner (LSW). (Accepted June 25, 1998)     

Optimization of a Thin-Walled,Anisotropic Curved Bar for Maximum Torsional Stiffness∗

ABSTRACT

ABSTRACT A curved bar in the form of a circular ring sector is under uniform torsion when acted upon by two equal and opposite forces directed alone the axis passing through the center of the ring and perpendicular to its plane, i.e., forces acting along the axis of rotation. The exact torsion theory can be extended to this case when the material of which the bar consists is cylindri-cally anisotropic, with the axis of anisotropy directed along the axis of rotation and having an elastic symmetry about any plane of the transverse cross section. In this paper, a thin-walled curved bar having the loading conditions and material properties described above is optimized so as to maximize its torsional stiffness. The optimization is carried out with respect to the cross-sectional shape of the bar subject to constraints on the transverse area (single-purpose design) and bending stiffness (multipurpose design). In the special case of an orthotropic material, the angle of inclination of the ortho-tropy axes with respect to the middle plane is optimally determined for a cross section with constant thickness. A perturbation method is used to obtain analytical solutions, and numerical results are presented indicating the efficiency of the designs and the optimal cross-sectional shapes.