On finite element large displacement and elastic-plastic dynamic analysis of shell structures

Finite element procedures for nonlinear dynamic analysis of shell structures are presented and assessed. Geometric and material nonlinear conditions are considered. Some results are presented that demonstrate current applicabilities of finite element procedures to the nonlinear dynamic analysis of two-dimensional shell problems. The nonlinear response of a shallow cap, an impulsively loaded cylindrical shell and a complete spherical shell is predicted. In the analyses the effects of various finite element modeling characteristics are investigated. Finally, solutions of the static and dynamic large displacement elastic-plastic analysis of a complete spherical shell subjected to external pressure are reported. The effect of initial imperfections on the static and dynamic buckling behavior of this shell is presented and discussed.     

On some current procedures and difficulties in finite element analysis of elastic-plastic response

Some finite element procedures for the analysis of elastic-plastic response are presented and critically discussed: a consistent large displacement and large strain formulation is summarized, a versatile elastic-plastic model applicable to the analysis of metals and geological materials is presented, the choice of an appropriate finite element discretization is discussed, and some effective methods for the solution of the nonlinear finite element equations are briefly summarized. Finally, to illustrate the strength and shortcomings of the procedures used, the results of some sample analyses are presented and evaluated.     

Cyclic elastic-plastic dynamic analysis by the finite element method

A finite element approach for cyclic elastic-plastic dynamic analysis is presented. A hardening model suited for cyclic plasticity behavior is incorporated. It is composed of several yield surfaces, and nonlinear stress-strain curves can be included. The central difference timewise operator is employed to solve the equations of motion. Comparison is made with the Newmark operator. Numerical examples illustrate the effect of cyclic plastic deformations on the dynamic response of simple problems. Comparison is presented for the structural behavior as predicted by the present hardening model and by the isotropic hardening model.     

Cyclic elastic-plastic creep steady-state analysis by the finite element method

In this paper, a definition of generalized cyclic steady state and convergence criterion of cyclic steady state for numerical calculation are introduced. An incremental-iterative finite element analysis based on the modified Newton-Raphson method is used for the steady state analysis. The material model used for numerical computation is an extension of classical plasticity theory which accounts for nonisothermal effect and creep behavior. In addition, two numerical examples are presented to demonstrate different types of cyclic steady states.     

An elastic-plastic finite element analysis of a CT fracture specimen

Two- and three-dimensional finite element calculations are presented for a 1TCT-specimen. The constitutive equations of the material are based upon the v. Mises yield criterion with isotropic hardening considering different hardening moduli. The results are compared with other finite element calculations and with experimental data. The agreement is quite good. It is confirmed that the state of stress in a 1TCT-specimen tends more to plane stress than to plane strain behaviour. Recommendations for the application of ADINA to this class of problems are given.     

Direct solution vs quadratic programming technique in elastic-plastic finite element analysis

Elastic-plastic plane stress finite element analysis of a disk rolling on a rigid track is performed by the direct method as well as the quadratic programming technique. Tresea and von Mises' yield conditions are used in the former whereas an approximate piecewise linear Tresea yield condition is used in the later case. It is concluded from a comparison of the computer times needed in the two cases that the direct method is far superior to the quadratic programming technique.     

Efficient elastic-plastic finite element analysis with higher order stress-point algorithms

The treatment of elastic-plastic problems with finite elements depends essentially on the methods used for state determination and the solution of the nonlinear equations. A systematic formulation of the state determination leads to higher order algorithms, which can better satisfy demands on accuracy and computational costs. The state determination influences highly the solution method for the system of nonlinear equations. In a comparison between Newton and a quasi-Newton method it is shown, that quasi-Newton methods are more suited for an efficient computation in combination with accurate path independent state determination algorithms.     

A numerically expedient scheme for elastic-plastic calculations in incremental finite element analysis

A numerically expedient scheme developed by Yang [1]for the modification of a Cholesky decomposed stiffness matrix is outlined. When used in conjunction with an incremental elastic-plastic finite element program, this method may result in a substantial reduction of computer time. The technique is appropriate for small strain problems, and optimal benefits are realized in situations involving contained plastic flow. The numerical efficiency of the technique is substantiated by case studies.     

Analysis of two-dimensional mixed-mode crack problems by finite element alternating method

A finite element alternating method is presented and applied to analyze two-dimensional linear elastic mixed-mode fracture problems with single or multiple cracks. The method involves the iterative superposition of the finite element solution of a bounded uncracked plate and the analytical solution of an infinite two-dimensional plate with a crack subjected to arbitrary normal and shear loadings. The normal and shear residual stresses evaluated at the location of fictitious cracks are fitted by appropriate polynomials through the least-squares method. Based on those coefficients of the determined polynomials, the mixed-mode stress intensity factors can be calculated accurately. The interaction effects among cracks are also considered. This method provides a highly efficient way to deal with two-dimensional fracture problems.     

Effect of finite element choice in blunt crack band analysis

The previously developed method of element-wide blunt smeared crack bands, which allows an effective finite element analysis of cracks that are not fixed but propagate and do so in any direction, has so far been numerically studied and demonstrated only for the constant-strain triangular elements. Here this is accomplished for linear strain triangles and for all three methods developed in [1], including the methods of energy variation, of equivalent strength, and of fitting asymptotic series to nodal displacements. Meshes of greatly different sizes are shown to give again the same results except for a negligible error; this indicates satisfactory convergence. Accuracy of the stress intensity factor, compared to the exact solutions for sharp cracks, is found to be sufficient but not better than that achieved previously with constant strain triangles. However, the accuracy may well be better in case of concrete structures in which the element-wide crack band serves not merely as a convenient approximate representation of a sharp crack but as a better representation of the actual fracture process.     

An efficient and accurate alternative to subincrementation for elastic-plastic analysis by the finite element method

In this paper a new and efficient alternative to subincrementation is developed for analysis of solid media with rate independent elastic-plastic material behavior. This alternative method is not unlike the subincrementation procedure in that it represents an Euler integration of the nonlinear constitutive equations. However, it takes advantage of the fact that the Euler integration procedure assumes proportional loading steps so that when the uniaxial stress-strain curve is idealized as a piecewise linear relation very large forward integration steps give accurate results. The new procedure, which we call the ζ method, is equally appropriate for cyclic loading with combined isotropic and kinematic hardening. However, due to the nonuniqueness of the monotonic uniaxial stress-strain relation in rate dependent media, the method is not appropriate for use in viscoplastic media. Although the algorithm deals only with the evaluation of a classical plasticity based constitutive law, numerical results are reported herein for an assortment of problems by the finite element method. It is shown via these results that the ζ method discussed herein provides not only accuracy which is superior to the subincrementation method, but the resulting algorithm also shows improved numerical efficiency.     

Automated optimization of transverse frame layouts for ships by elastic-plastic finite element analysis

This paper presents a model for the optimum design of ship transverse frames. An elastic-plastic finite element analysis algorithm for plane frames has been incorporated in the model to evaluate the ultimate strength of the overall frame, and different effects of design loads. Using these strengths and load effects, appropriate design constraints are then formulated to prevent different failure categories; the overall collapse, ultimate limit state failures and serviceability failures. Possible instabilities and effects of combined loads are accounted for in formulating these constraints. Scantlings of the frame structure have been modelled as free design variables. The weight function and different constraint functions are then derived relating design variables in such a way that once parameters for finite element analysis are input, the scheme automatically forms the objective function and all constraints, and then interacts with the simplex algorithm through sequential linearization to find the optimum solution. Thus the scheme is almost automatic. Different layouts of the frame structure have been designed by executing this scheme, which demonstrates the capability of the model and the possibility of weight savings by choosing the appropriate layout. Finally, it is suggested how this model would interact with the design of longitudinal materials to ensure the overall optimality in ship hull module design, to prevent grillage buckling and to validate underlying assumptions in analysis.     

A simple finite element model for elastic-plastic plate bending

A consistent finite element model for a plate is developed based on triangular elements and a piecewise-linear displacement field. The resulting generalized stresses are the average normal moments across the element interfaces. Equilibrium equations are derived for each node, and a simple constitutive equation is obtained for each generalized stress. Applications are made to some square plate problems.     

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.     

Concurrent finite element analysis of periodic boundary value problems

A parallel finite element approach for analyzing micromechanical problems with periodic unit cells is discussed. The method uses a direct solution strategy so that general periodic boundary conditions can be treated using a two-step domain decomposition strategy. The speedup results show a good performance of the method on coarse-grained problems, i.e. for cases where the computational work done on the substructures that are treated in parallel is relatively large compared to the total amount of computational work. Application examples using crystal-plasticity on an array of planar crystals and a metal matrix composite are used to show that the overall response of these materials is rather strongly dependent on the constraint imposed on the unit cell so that a correct treatment of the periodic boundary conditions is required to accurately predict the macroscopic response of a periodic material even though a unit cell with a large number of grains or fibers is used.     

Probability of failure models in finite element analysis of brittle materials

A model of failure for brittle materials is presented, based on the weakest link hypothesis and Weibull distribution function. Methods of computing the probability of failure of a structural component, and numerical implementation in a finite element program, are shown. Computer subroutines are included.     

Three dimensional finite element analysis of layered fiber-reinforced composite materials

A three-dimensional finite element analysis was performed for a biaxially loaded composite laminate (with a centered hole) consisting of several fiber-reinforced composite layers each with a specified fiber orientation. The detailed stress distribution around the hole was determined. Also, the locations of initial damage zones due to different failure mechanisms were indicated.     

On the finite element creep rupture analysis of structures

The analysis of problems involving creep rupture is considered. Two creep material failure criteria are employed, i.e. the Kachanov-Rabotnov damage relations and a new, in conjunction with the finite element method, energy criterion.Calculations are reported for titanium notched tensile specimens, where the plastic strains are evaluated by the Ramberg-Osgood formulas.