Large displacements in-plane analysis of elastic-plastic frames

A large displacement theory for in-plane elastic plastic frames is formulated. The derivation is based on incremental variational principle using TLA formulation. A beam element with local-global DOF is used in the analysis. The method of solution of the FEM equations is related to computation in the load-configuration space R^N+1.

Results of two numerical examples are compared with classical solutions.     

Large deformation of nonlinear elastic nanofilms with surface energy

Microsystem Technologies - The influence of nonlinear elasticity on the bending of nanofilms under transverse load has been studied. The effects of second order elasticity, surface energy and large...     

Free vibration analysis of beams on elastic foundation

A simple finite element method is developed and applied to treat the free vibration analysis of beams supported on elastic foundations. The entire analysis is programmed to run on a microcomputer and with few elements modelling the beam, gives quick and reliable results. Numerical examples pertaining to the free vibration of beams in some special situations are considered, such as a stepped beam on an elastic foundation, beam on a stepped elastic foundation and a continuous beam on an elastic foundation. Present results compare very well with those obtained from existing solutions, wherever possible.     

Large deformation analysis of ellipsoidal head pressure vessels

Among the most common pressure vessels, the elliptical head pressure vessel stands out to be the second best in order of preferable stress distribution at the head-cylinder junction—the best being hemispherical head. But, like others, the deformation at the head-cylinder junction of this pressure vessel is so large that the stress distribution obtained from linear shell theory is far off from reality. The nonlinear shell equations of ellipsoidal head pressure vessels are solved here using the multisegment method of integration, developed by Kalnins and Lestingi[11]. Reissner's nonlinear equations for the axisymmetric deformation of shells of revolution, after specialization for ellipsoidal shells and further necessary modification for avoiding geometrical singularity at the apex of the head are used in this analysis. It is shown that the linear theory consistently over estimates the stresses at the head-cylinder junction of ellipsoidal head pressure vessels.     

Moving finite element analysis for the elastic beams in contact problems

The contact problem of a linear elastic beam with a rigid barrier is considered, in which the contact surface is assumed to be frictionless. The problem contains the characteristic of moving boundaries as the contact regions expand or reduce in size when the external loads alter. Starting from the variational principles, we derived the interface equations as well as the governing equation. In addition to matching the deflections and the slopes with the rigid barrier at the marginal nodes of the contact regions, the interface equations also have to be satisfied there. In essence, the interface equations are designed to locate the unknown and moving marginal nodes. Although it is confined within the framework of small deformation and linear elastic material behavior, the problem exhibits high nonlinearity due to the moving nature of the marginal nodes. In this paper, we present a moving finite element analysis employing incremental procedures and an iterative numerical scheme to tackle the problem. A fixed number of two-node beam elements are used in the moving finite element analysis and the size of the elements varies as the loads alter. A couple of examples, whose exact solutions are obtainable, are chosen to demonstrate the accuracy and efficiency of the proposed numerical algorithm.     

Analysis of beams on non-homogeneous elastic foundation

An approximate method is developed to study the bending of the beam on non-homogeneous elastic foundation. The solutions are obtained by translating the differential equations into the integral equations and applying the numerical integrations. It is shown that we can analyze the beams with arbitrary boundary conditions and load conditions resting on non-homogeneous elastic foundation.     

Analysis of beams on BI-moduli elastic foundation

The analysis of beams on elastic foundation using the Winkler model is very common in engineering. When an elastic foundation is incapable of exerting tensile reactions, or when it has different stiffnesses in compression and tension, the simple Winkler model leads to a set of nonlinear equations which are complicated even for simple cases. Using exact stiffness matrices for beams on elastic foundation the problem is solved in an iterative technique, in which secondary nodes are inserted at transition points. Comparisons are made with simple case results in literature and the efficiency of the proposed procedure is demonstrated for a complex loading system.     

Analysis of elastic beams on nonlinear foundations

The midpoint difference method is organized for solving the basic differential equation for the elastic deformation of a beam supported on an elastic, nonlinear foundation with rigid or elastic descrete supports. An iterative approach is used in solving the nonlinear problem; a weighted averaging scheme is employed to speed up the convergence to a solution. The method of analysis, as programmed for a computer solution, considers the continuous elastic, nonlinear foundation to be active only when the beam is pressing against the foundation; the foundation is assumed to be inactive in the regions where the beam has displaced away from the foundation. Two examples are presented to illustrate the application of the method of analysis.     

On the optimal design of elastic beams

In this paper we investigate the optimal dynamics of simply supported nonlinearly elastic beams with rectangular cross-sections. We consider the elastic beam under the assumption of time-dependent intensive transverse loading. The state of the beam is described by a system of partial differential equations of the fourth order. We deal with the problem of choosing the optimal shape for the beam. The optimal shape is determined in such a way that the deflection of the nonlinearly elastic beam for any given time is minimal. The problem of choosing the optimal shape is formulated as an optimal control problem. To solve the obtained problem effectively, we use the optimality principle of Bellman (Bellman and Dreyfus 1962; Bryson and Ho 1975) and the penalty function method (Polyak 1987). We present a constructive algorithm for the optimal design of nonlinearly elastic beams. Some simple examples of the implementation of the proposed numerical algorithm are given.     

Large deformation elastic-plastic buckling analysis of spherical caps with initial imperfections

Large deformation elastic-plastic buckling loads are obtained for axisymmetric spherical caps with initial imperfections. The problem formulation is based on equilibrium equations in which the plastic deformation is taken as an effective plastic load. Both perfectly plastic and strain hardening behavior are considered. Strain hardening is represented by the Prager-Ziegler kinematic hardening theory, so that the Bauschinger effect is accounted for. Solutions of elastic-plastic circular plates and spherical caps are in good agreement with previous results. For the spherical cap it was determined that both initial imperfection and plastic deformation have the same effect of reducing buckling capacity; as the magnitude of the imperfection increases, the influence of plastic deformation becomes less important. It is also found that the geometric parameter λ, which is used as an important factor in elastic response, becomes meaningless for the elastic-plastic buckling analysis of spherical caps.     

Large deformation static and dynamic finite element analysis of extensible cables

Approximate numerical integration of the element total potential energy with polynomial interpolation of the displacements creates high order nonlinear, extensible, cable finite elements. Successful computations of static and dynamic large displacement cable problems are carried out with the element.     

A finite element analysis of beams on elastic foundation including shear and axial effects

A displacement finite element method for analyzing a beam on continuous elastic foundation is presented. A three-dimensional model which accounts for the effects of both the Filonenko-Borodich and Pasternak foundation models in a consistent and complete way is used. A variational principle is introduced with the slope field due to bending only and the displacement field approximated by independent quantities subjected to variation. Numerical examples illustrate the accuracy of the element, the importance of shear, axial and shear-axial interaction effects associated with continuous elastic foundation, and finally the application of the element to a rotor supported by two hydrodynamic journal bearings.     

Optimization of elastic spring supports for cantilever beams

Structural and Multidisciplinary Optimization - In this study,a new approach of optimization algorithm is developed. The optimum distribution of elastic springs on which a cantilever Timoshenko...     

轴向受力梁结构线弹性碰撞问题求解

研究了质点对轴向受力的Euler-Bernoulli梁结构任意位置的横向撞击问题.把撞击体系简化为质量-弹簧体系模型,采用积分变换方法,对撞击体系的控制微分方程、边界条件和连续条件进行Laplace变换,在频域内求得其解析表达式,然后采用Crump逆变换方法进行数值反演,得到时域内的各种动力响应.数值算例给出了撞击力、弯曲应力和剪力随时间变化的曲线,通过与有限元比较验证了本方法的正确性.最后研究了撞击位置、轴向压力、撞击质量、撞击速度和柔度系数等参数对撞击力的影响,得出了一些有用的结论.     

Exact stiffness matrix for beams on elastic foundation

An exact stiffness matrix of a beam element on elastic foundation is formulated. A single element is required to exactly represent a continuous part of a beam on a Winkler foundation. Thus only a few elements are sufficient for a typical problem solution. The stiffness matrix is assembled in a computer program and some numerical examples are presented.     

Exact matrices for beams on three-parameter elastic foundation

In the present paper, the process of the formulation of the stiffness and transfer matrices and of the load vectors of Timoshenko beams on Kerr-type three-parameter elastic foundation is presented. These matrices are developed on the basis of the exact solution of the governing differential equations for all potential solution cases. The reliability and precision of the modeling of beams resting on elastic foundation through the use of these matrices is assessed by means of two numerical examples.     

弹性梁点控制、点测量与指数镇定

运用近年来发展的基理论对弹性梁点测量、点控制做一个系统的处理, 得到了用速度线性反馈可实现系统的指数镇定的条件且指数镇定当且仅当系统精确可控, 在指数镇定的情况下闭环系统的广义本征函数生成能量空间的Riesz基且谱确定增长条件成立.