Finite element analysis of elasto-plastic plate bending problems using transition rectangular plate elements

In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based on a practical rule. The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements. The mesh convergence rates of the models including the transition elements are compared with the regular element models. To verify the developed elements, simple tests are demonstrated and various elasto-plastic problems are solved. Their results are compared with ANSYS results.

EFFECTIVE NUMERICAL METHODS FOR ELASTO-PLASTIC CONTACT PROBLEMS WITH FRICTION

Several effective numerical methods for solving the elasto-plastic contact problems with friction are pres- ented.First,a direct substitution method is employed to impose the contact constraint conditions on condensed finite ele- ment equations,thus resulting in a reduction by half in the dimension of final governing equations.Second,an algorithm composed of contact condition probes and elasto-plastic iterations is utilized to solve the governing equation,which distinguishes two kinds of nonlinearities,and makes the solution unique.In addition,Positive-Negative Sequence Modifica- tion Method is used to condense the finite element equations of each substructure and an analytical integration is intro- duced to determine the elasto-plastic status after each time step or each iteration,hence the computational efficiency is en- hanced to a great extent.Finally,several test and practical examples are pressented showing the validity and versatility of these methods and algorithms.

A THEORETICAL SOLUTION OF CYLINDRICAL SHELLS FOR AXISYMMETRIC PLAIN STRAIN ELASTODYNAMIC PROBLEMS

A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special Junction was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties of Bessel Junctions, the equation With respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface.

A GENERAL SOLUTION OF AXISYMMETRIC PROBLEM OF ARBITRARY THICK SPHERICAL SHELL AND SOLID SPHERE

In this paper, the axisymmetric problems of arbitrary thick spherical shell and solid sphere are studied directly from equilibrium equations of three-dimensional problem, and the general solutions informs of Legendre serifs for thick spherical shell and solid sphere are given by using the method of weighted residuals.

AXISYMMETRIC PROBLEMS OF CYLINDRICAL SHELLS WITH VARIABLE WALL THICKNESS

The purpose of this paper is to give the general solutions for axisymmetric eylindrical shells with paraholically varying wall thickness.

EQUATION IN COMPLEX VARIABLE OF AXISYMMETRICAL DEFORMATION PROBLEMS FOR A GENERAL SHELL OF REVOLUTION

In this paper, the equation of axisymmetrical deformation problems for a general shell of revolution is derived in one complex variable under the usual Love-Kirchhoff assumption. In the case of circular ring shells, this equation may be simplified into the equation given by F.Tdlke(1938)[3]. R.A. Clark(1950 )[4] and V. V.Novozhilov(1951)[5]. When the horizontal radius of the shell of revolution is much larger than the average radius of curvature of meridian curve, this equation in complex variable may be simplified into the equation for slander ring shells. If the ring shell is circular in shape, then this equation can be reduced into the equation in complex variable for slander circular ring shells given by this author (1979)[6]. If the form of elliptic cross-section is near a circle, then the equation of slander ring shell with near-circle ellipitic cross-section may be reduced to the complex variable equation similar in form for circular slander ring shells.

A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.

Markov Chain Monte Carlo Solution of Laplace’s Equation in Axisymmetric Homogeneous Domain

With increasing complexity of today’s electromagnetic problems, the need and opportunity to reduce domain sizes, memory requirement, computational time and possibility of errors abound for symmetric domains. With several competing computational methods in recent times, methods with little or no iterations are generally preferred as they tend to consume less computer memory resources and time. This paper presents the application of simple and efficient Markov Chain Monte Carlo (MCMC) method to the Laplace’s equation in axisymmetric homogeneous domains. Two cases of axisymmetric homogeneous problems are considered. Simulation results for analytical, finite difference and MCMC solutions are reported. The results obtained from the MCMC method agree with analytical and finite difference solutions. However, the MCMC method has the advantage that its implementation is simple and fast.

Local Solution of Three-Dimensional Axisymmetric Supersonic Flow in a Nozzle

In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilinear hyperbolic system to solve this problem. The boundary value condition is set in particular to guarantee the character number condition. By this trick, the theory in quasilinear hyperbolic system can be employed to a large range of the boundary value problem.

A THEORETICAL SOLUTION FOR AXIALLY SYMMETRIC PROBLEMS IN ELASTODYNAMICS

This paper presents a theoretical solution for the basic equation of axisymmetric problems in elastodynamics.The solution is composed of a quasi-static solution which satisfies inhomogeneous boundary conditions and a dynamic solution which satisfies homogeneous boundary conditions.After the quasi-static so- lution has been obtained an inhomogeneous equation for dynamic solution is found from the basic equation. By making use of eigenvalue problem of a corresponding homogeneous equation,a finite Hankel transform is defined.A dynamic solution satisfying homogeneous boundary conditions is obtained by means of the finite Hankel transform and Laplace transform.Thus,an exact solution is obtained.Through an example of hollow cylinders under dynamic load,it is seen that the method,and the process of computing are simple,effective and accurate.

Unified characteristics line theory of spacial axisymmetric plastic problem

The unified strength theory proposed by Yu in 1991 is extended to spacial axisymmetric problem. A unified spacial axismymmetric characteristics line theory based on the unified strength theory is proposed. This theory takes account of different effects of intermediate principal stress on yielding or failure and the SD effect (tensile-compression strength difference) of materials. Various conventional axisymmetric characteristics line theories, which are based on the Haar-von Karman plastic condition, Szczepinski hypothesis, Tresca criterion, von Mises criterion and Mohr-Coulomb theory, are special cases of the new theory. Besides, a series of new spacial axisymmetric characteristics fields for different materials can be introduced. It forms a unified spacial axisymmetric characteristics theory. Two examples are calculated with the new theory, the results are compared with those obtained by the finite element program UEPP and those based on the Mohr-Coulomb strength theory. It is shown that the new theory is reliable and feasible. The economic benefit can be obtained from the engineering application of the new theory.

An axisymmetric characteristic model for enhancing prediction of centrifugal compressor characteristics

Rapid and accurate determination of compressor characteristic maps is essential for the initial design of centrifugal compressors in aircraft power systems. The accuracy of existing methodologies, which rely on combinations of loss models, varies significantly depending on the compressor's geometry and operational range. This variance necessitates substantial experimental or Computational Fluid Dynamics(CFD) data for coefficient calibration. To address this challenge, this study presents an axisymmetric characteristic model for compressor performance assessment. This model incorporates the factors of blade angle, meridional passage area, and the radial deflection angle of meridional streamlines of the compressor. These factors are derived from fundamental aerodynamic equations encompassing mass, momentum, and energy conservation of the compressor. In contrast to conventional one-dimensional approaches, the proposed method reduces the number of loss coefficients and more effectively accounts for the impact of geometric alterations on centrifugal compressor properties. Furthermore, the model reduces dependence on experimental and CFD data. Efficacy of the model is validated using experimental data from four distinct types of centrifugal compressors. Correlation analysis reveals that the model's coefficients can be expressed as functions of the ratio of the Reynolds number to the impeller tip speed. This ratio serves as a characteristic parameter for the design and optimization of centrifugal compressors. Consequently, the proposed method offers an efficient and accurate means for the quick computation of centrifugal compressor characteristics. This is of great significance for improving the efficiency of centrifugal compressors and reducing energy consumption.

Completeness of General Solutions to Axisymmetric Problems of Transversely Isotropic Body

In this paper a kind of problems,which are a little wider than the axisymmetric problems of a transversely isotropic elastic body,are considered in a rectangular coordinates system.Two new general solutions of the axisymmetric problems of a transversely isotropic body are concisely obtained in a cylindrical coordinates system.Their completeness is also proved.It is worth while pointing out thai whether the meridional half-section is simply connected or multiply connected,both the new general solutions are single-valued.Using these results eight special general solutions are derived,including some known famous solutions.

Three-dimensional non-axisymmetric Lamb' s problem for saturated soil

Based on the integral transformation method with which the combinatory integral transform of the displacements and the combinatory integral transform of the stresses are presented, the three-dimensional (3-D) non-axisymmetric governing dynamic equation in the Biot’s theory of two-phase medium is solved. Integral solutions with the soil skeleton displacements and pore pressure as the main unknown quantity are obtained. On the basis of this solution, a systematic study on Lamb’ s problems for saturated soils is performed. Considering the case of drained surface and the case of undrained surface, the integral solutions for surface radial, vertical and circumferential direction displacements under the vertical surface force and horizontal surface force are obtained, which would be reduced to the solutions of the classical Lamb’s problem. So, the correctness of the solutions would be verified. The numerical example indicates that the two-dimensional (2-D) model cannot be applied to 3-D problem accurately.

Numerical Approximation of an Axisymmetric Elastoacoustic Eigenvalue Problem

This paper deals with the numerical approximation of a pressure/displacement formulation of the elastoacoustic vibration problem in the axisymmetric case.We propose and analyze a discretization based on Lagrangian finite elements in the fluid and solid domains.We show that the scheme provides a correct approximation of the spectrum and prove quasi-optimal error estimates.We report numerical results to validate the proposed methodology for elastoacoustic vibrations.

The Method of Fundamental Solutions for Solving Exterior Axisymmetric Helmholtz Problems with High Wave-Number

In this paper,we investigate the method of fundamental solutions(MFS)for solving exterior Helmholtz problems with high wave-number in axisymmetric domains.Since the coefficientmatrix in the linear system resulting fromtheMFS approximation has a block circulant structure,it can be solved by the matrix decomposition algorithm and fast Fourier transform for the fast computation of large-scale problems and meanwhile saving computer memory space.Several numerical examples are provided to demonstrate its applicability and efficacy in two and three dimensional domains.

预应力锚杆作用机制研究

针对预应力锚杆作用机制研究方面存在的问题,根据弹性理论轴对称问题的基本理论和方法,在引入锚杆影响范围内岩体平均轴向应力(平均轴向应变)假设的条件下,推导锚杆在完全黏结条件下界面剪应力分布公式;以此为基础,在考虑界面本构关系情况下,研究界面脱黏段的剪应力分布及脱黏段长度,阐述预应力锚杆的荷载传递特性,从而为预应力锚杆设计提供理论依据。

圆柱壳的轴对称平面应变弹性动力学解

给出一种圆柱壳的轴对称平面应变弹性动力学问题的解析方法· 首先通过引入一特定函数将非齐次边界条件化为齐次边界条件 ,然后利用分离变量法将位移减去特定函数的量展开为关于贝塞尔函数和时间函数乘积的级数 ,并由贝塞尔函数的正交性 ,导出时间函数的方程 ,容易求得此方程的解· 将两者叠加可得弹性动力学问题的位移解· 运用此方法 ,可以避免积分变换 。

解析层元法求解层状横观各向同性地基轴对称问题

提出了一个求解横观各向同性层状地基轴对称问题的解析层元方法。从弹性力学基本方程出发并利用Hankel变换,得到横观各向同性单层地基的传递矩阵解,进而推导出单层地基的解析层元刚度矩阵。利用有限元方法组装总体刚度矩阵,通过求解总体刚度矩阵,并采用Hankel逆变换的数值积分方法,可求出层状横观各向同性弹性体轴对称问题在物理域内的精确解。刚度矩阵元素中不存在正指数并具有对称的特点,不仅使计算过程简化,还提高了计算精度。最后文中给出了算例来证明推导结果的准确性。