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.     

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.     

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.     

Finite element stress formulation for dynamic elastic-plastic analysis

The solution to wave propagation problems in solids with elastic-plastic material properties is obtained by using the finite element method directly in terms of the stresses. A variational principle due to Gurtin is modified by including a plastic strain tensor in the constitutive relationship. The resulting finite element equations, which represent the strain-displacement equations written in terms of the stresses, are simultaneous integral equations in time. With a transformation of variables, a set of simultaneous differential equations is obtained of the form$\text{H}\text{s}\text{?}\text{+ Qs+ Ve}{}_{\mathrm{p}}\text{= q(t)}$, where $\text{H}$ is a symmetric positive-semidefinite matrix, and $\text{Q}$ is a symmetric positive-definite matrix. The stresses and the plastic strains are represented by $\text{s}\text{?}$ and $\text{e}{}_{\mathrm{p}}$, respectively.Finite element equations are developed for an axisymmetric ring element with an arbitrary quadrilateral cross section in which the stresses and the plastic strains vary linearly along the sides of the elements. The equations are numerically integrated with respect to time by Newmark's generalized acceleration method.An iterative procedure is presented, which uses the finite element strain-displacement equations and the plasticity relationships, to determine the state of stress at the end of the time step. Several examples are used to demonstrate the solution technique for elastic and elastic-plastic problems.     

Finite element analysis of dynamic quasi-bifurcations in elastic-plastic structures

Some numerical results related to the critical behavior of inelastic structures subjected to dynamic step loading are given. The underlying theory of dynamic quasi-bifurcations is adapted to the analysis of elastic-plastic solids. Two examples, a 2D truss and a plane stress column-like structure, are discussed at length.     

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.     

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.     

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.     

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.     

Reduction method for finite element dynamic analysis of submerged turbomachinery wheels

The proposed method allows the efficient computation of natural frequency mode shape and harmonic response of submerged rotationally periodic structures, such as turbine or centrifugal pump wheels. The geometry of such structures is complex and the influence of the surrounding fluid has to be taken into account. The fluid is assumed to be incompressible and at rest. Both fluid and structure domains are modelled using the finite element method. The size of the problem is appreciably reduced using the properties of wave propagation in periodic systems combined with modal techniques. The efficiency of the method is shown by an application to a submerged centrifugal pump wheel where the numerical results are compared to experimental results.     

Convective heat transfer analysis by the finite element method

A numerical procedure based on the finite element method is developed for the analysis of general two-dimensional problems in free/forced convection heat transfer. The dicretization of the field equations through use of the Galerkin method is described. Solution methods for both types of steady state convection are presented.The utility and accuracy of the described method is demonstrated through the solution of diverse examples illustrating both forced and free convection analysis. The use of temperature-dependent material properties and the inclusion of solid body conduction effects are also demonstrated.     

Elastic-viscoplastic analysis of plates by the finite element method

In this paper the finite element technique is employed in the solution of elastic-viscoplastic plate bending problems. The method is applicable to both thick and thin plates and by attaining steady-state conditions the process offers an alternative method of solution for static elasto-plastic situations. A quadratic isoparametric element based on Mindlin plate theory is adopted and the Euler time-stepping scheme is employed in solution. Yield criteria are based on moment resultants and the Von Mises, Tresca and Johansen forms are included. Several numerical examples are presented and the results compared with those from other sources where available     

A finite element method for elastic-plastic beams and columns at large deflections

A finite element scheme for the large-displacement analysis of elastic-plastic beams and columns is presented. The proposed method, which assures continuous deflections and continuous slopes at the element junctions, is shown to furnish fairly accurate results with a minimal number of elements. Comparisons are made with existing results for laterally loaded beams on elastic foundations and for elastic columns on bi-linear elastoplastic foundations. The effect of imperfections on the buckling of elastic-plastic columns is also investigated.     

On the finite element analysis of crack and inclusion problems in elastic-plastic materials

A finite element method for treating plane strain, elastic-plastic boundary value problems is described. Constant strain triangular elements are used. The material is assumed to obey the von Mises yield criterion and its associated flow rule. In order to test the accuracy of the method the deformation of a pressurized circular tube is investigated and the results are compared with a finite-difference solution. The applicability of the method to problems involving two different materials is demonstrated for the case of a uniaxially loaded plate containing a circular inclusion. Finally some crack problems are analysed. Special attention is devoted to the case of small scale plasticity.     

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.     

On a finite dynamic element method for free vibration analysis of structures

This paper explores the concept of finite dynamic elements involving higher order dynamic correction terms in the associated stiffness and mass matrices. Such matrices are then developed for a rectangular prestressed membrane element. Next, efficient analysis techniques for the eigenproblem solution of the resulting quadratic matrix equations are described in detail. These are followed by suitable numerical examples which indicate that employment of such dynamic elements in conjunction with an efficient quadratic matric solution technique will result in a most significant economy in the free vibration analysis of structures.     

Postbuckling analysis of elastic structures by the finite element method

An asymptotic method based on Koiter's elastic stability theory is presented for geometrically nonlinear structure analysis; these structures are subjected to a proportional applied load system. An approach that makes possible the choice of the modes which are necessary to obtain a good representation of the reduced energy is developed as an iterative process. The approach is transferred into the framework of the finite element method. Applied to the study of thin walled structures through some sample tests, the method gives, at low cost, numerical results which are in good agreement with the preceding studies.     

Periodic tidal flow analysis by finite element perturbation method

The numerical analysis of periodic tidal flow is presented. The present paper investigates a numerical procedure based on the mixed approach of the finite element method and the perturbation method by postulating periodic motion. Several numerical studies are presented to examine the validity of the formulation.     

Analysis of nonlinear, dynamic coupled thermoviscoelasticity problems by the finite element method

This investigation deals with the numerical solution of a class of nonlinear problem in transient, coupled, thermoviscoelastidty. Equations of motion and heat conduction are derived for finite elements of thermomechanically simple materials and these are adapted to special classes of thermorheologically simple materials. The analysis involves the solution of large systems of nonlinear integrodifferential equations in the nodal displacements and temperatures and their histories. As a representative example, the general equations are applied to the problem of transient response of a thick-walled hollow cylinder subjected to time-varying internal and external pressures, temperatures, and heat fluxes. The integration scheme used to solve the nonlinear equations employs a linear acceleration assumption, representation of nonlinear integral terms by Simpson's rule, and the iterative solution of large systems of nonlinear algebraic equations at each reduced time step by the Newton-Raphson method. Various numerical results are given and are compared with the linearized, isothermal, and quasi-static solutions.     

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.