Material Nonlinear Problems Research Articles

Technical Regulation for Numerical Simulation on Processing Technology of Large Forgings

The technical regulation for numerical simulation on processing technology of large forgings has entered into official supporting of National Key Special Project. This paper describes the outline of drafting the regulation. Special concerns are paid how to get a reliable numerical simulation result from material properties, nonlinear problems, convergence and verification, etc. Some main issues are pointed out and discussed.

Partial Refactorization in Sparse Matrix Solution: A New Possibility for Faster Nonlinear Finite Element Analysis

This paper proposes a partial refactorization for faster nonlinear analysis based on sparse matrix solution, which is nowadays the default solution choice in finite element analysis and can solve finite element models up to millions degrees of freedom. Among various fill-in’s reducing strategies for sparse matrix solution, the graph partition is in general the best in terms of resultant fill-ins and floating-point operations and furthermore produces a particular graph of sparse matrix that prevents local change of entries from wide spreading in factorization. Based on this feature, an explicit partial triangular refactorization with local change is efficiently constructed with limited additional storage requirement in row-sparse storage scheme. The partial refactorization of the changed stiffness matrix inherits a big percentage of the original factor and is carried out only on partial factor entries. The proposed method provides a new possibility for faster nonlinear analysis and is mainly suitable for material nonlinear problems and optimization problems. Compared to full factorization, it can significantly reduce the factorization time and can make nonlinear analysis more efficient.

A two-level parallel algorithm for material nonlinearity problems

An efficient two-level domain decomposition parallel algorithm is suggested to solve large-DOF structural problems with nonlinear material models generating unsymmetric tangent matrices, such as a group of plastic-damage material models. The parallel version of the stabilized bi-conjugate gradient method is developed to solve unsymmetric coarse problems iteratively. In the present approach the coarse DOF system is solved parallelly on each processor rather than the whole system equation to minimize the data communication between processors, which is appropriate to maintain the computing performance on a non-supercomputer level cluster system. The performance test results show that the suggested algorithm provides scalability on computing performance and an efficient approach to solve large-DOF nonlinear structural problems on a cluster system.

Rheological-dynamical analogy: design of viscoelastic and viscoplastic bar dampers

An analytical procedure is developed for computing the dynamic response of bar dampers using the rheological-dynamical analogy. This method is very efficient when applied to inelastic deformations, because it reduces a material nonlinear problem to a linear dynamical problem, which allows the use of modal analysis. Two types of damping are considered: viscous damping in the case of linear analysis; and hysteretic damping caused by inelastic deformations of the damper. Based on the formulas of the two types of damping, an iterative procedure for the design of viscoelastic and viscoplastic bar dampers is derived.

Mathematical modeling of materially nonlinear problems in structural analyses, Part II: Application in contemporary software

The paper presents application of nonlinear material models in the software package Ansys. The development of the model theory is presented in the paper of the mathematical modeling of material nonlinear problems in structural analysis (part I - theoretical foundations), and here is described incremental-iterative procedure for solving problems of nonlinear material used by this package and an example of modeling of spread footing by using Bilinear-kinematics and Drucker-Prager mode was given. A comparative analysis of the results obtained by these modeling and experimental research of the author was made. Occurrence of the load level that corresponds to plastic deformation was noted, development of deformations with increasing load, as well as the distribution of dilatation in the footing was observed. Comparison of calculated and measured values of reinforcement dilatation shows their very good agreement.

A meshless FPM model for solving nonlinear material problems with proportional loading based on deformation theory

In this work a methodology of meshless finite points method for the analysis of nonlinear material problems with proportional loading based on deformation theory is presented. In finite points method the approximation around each point is obtained by using weighted least square techniques. The discrete system of equation is constructed by means of a point collocation procedure. The non-dependence on a mesh or integration procedures is an important aspect which transforms the finite point method in a truly meshless technique. Hencky's total deformation theory and an elastic approach is used on the determination of stress-strain fields. This approach introduces the concept of effective material properties which are considered as spatial field variables and to be functions of equilibrium stress state and material properties. The present results are in good agreement with those obtained by nonlinear finite element method and previous work in this meshless context. Nevertheless the present methodology is based on a strong formulation, keeping the meshless characteristics of FPM.

Locking-free two-layer Timoshenko beam element with interlayer slip

A new locking-free strain-based finite element formulation for the numerical treatment of linear static analysis of two-layer planar composite beams with interlayer slip is proposed. In this formulation, the modified principle of virtual work is introduced as a basis for the finite element discretization. The linear kinematic equations are included into the principle by the procedure, similar to that of Lagrangian multipliers. A strain field vector remains the only unknown function to be interpolated in the finite element implementation of the principle. In contrast with some of the displacement-based and mixed finite element formulations of the composite beams with interlayer slip, the present formulation is completely locking-free. Hence, there are no shear and slip locking, poor convergence and stress oscillations in these finite elements. The generalization of the composite beam theory with the consideration of the Timoshenko beam theory for the individual component of a composite beam represents a substantial contribution in the field of analysis of non-slender composite beams with an interlayer slip. An extension of the present formulation to the non-linear material problems is straightforward. As only a few finite elements are needed to describe a composite beam with great precision, the new finite element formulations is perfectly suited for practical calculations.

A pseudo-elastic local meshless method for analysis of material nonlinear problems in solids

This paper aims to develop an effective meshless technique for the analysis of elasto-plastic problems. The material nonlinearity will be studied by a new pseudo-elastic local radial point interpolation formulation which is based on the local Petrov–Galerkin form and the radial basis function (RBF) interpolation. Hencky's total deformation theory is used to define the effective Young's modulus and Poisson's ratio, which are treated as spatial field variables, and considered as functions of the final stress state and material properties. These effective material parameters are obtained in an iterative manner using the strain controlled projection method. Several numerical examples are presented to illustrate the effectivity of the newly developed formulation, and the numerical results obtained by the present method closely agree with the results obtained by other methods. It has proven that the present pseudo-elastic local meshless method is effective and easy to apply to the analysis of elasto-plastic materials subjected to proportional loading.

Time discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium

A time-discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium is proposed. As compared with the existing discontinuous Galerkin finite element methods, the distinct feature of the proposed method is that the continuity of the displacement vector at each discrete time instant is automatically ensured, whereas the discontinuity of the velocity vector at the discrete time levels still remains. The computational cost is then obviously reduced, particularly, for material non-linear problems. Both the implicit and explicit algorithms to solve the derived formulations for material non-linear problems are developed. Numerical results show a good performance of the present method in eliminating spurious numerical oscillations and providing with much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in the time domain.

損傷力学手法に基づく複合材料機械的継手部の面圧破壊挙動シミュレーション

This paper presents the development of an accumulative damage model based on continuum damage mechanics (CDM) to simulate the bearing failure and response in the bolted composite joints. The simulation is implemented into a general-purpose FEM code ABAQUS. The main damage mechanisms observed from experimental study are described as accumulated compressive damage that appeared by matrix compression failure and fiber compression-shear failure. The fundamental approach consists of contact problem at the pin/hole interface, progressive damage, large deformation problem and material nonlinear problem. A complex approach based on a nonlinear shear elasticity theory combined with a continuum damage mechanics approach can be also utilized to represent the material nonlinear behavior during loading. The damage accumulation criteria using the hybrid method based on Hashin and Yamada-Sun’s failure criteria are adopted, and the stress redistribution analysis using a degradation model for the damaged ply is performed. The accurate prediction results include progressive damage and strength response of the joints that agrees well with the existing experimental data.

A vertex‐based finite volume method applied to non‐linear material problems in computational solid mechanics

AbstractA vertex‐based finite volume (FV) method is presented for the computational solution of quasi‐static solid mechanics problems involving material non‐linearity and infinitesimal strains. The problems are analysed numerically with fully unstructured meshes that consist of a variety of two‐ and three‐dimensional element types. A detailed comparison between the vertex‐based FV and the standard Galerkin FE methods is provided with regard to discretization, solution accuracy and computational efficiency. For some problem classes a direct equivalence of the two methods is demonstrated, both theoretically and numerically. However, for other problems some interesting advantages and disadvantages of the FV formulation over the Galerkin FE method are highlighted. Copyright © 2002 John Wiley & Sons, Ltd.

A Large Increment Method for Material Nonlinearity Problems

In the case of small deformation, cumulative errors and time consumption are the crux blocking the application of flow theory for material nonlinearity problems. To overcome these blockages, a new algorithm is proposed in the present paper. Different from traditional methods, the theory of generalized inverse of matrix and a new optimization approach are introduced to give full play of the force method. As one of the main advantages, parallel computation process is used to replace the step by step solution process. Time consumption are therefore reduced and cumulative errors suppressed in essence.

A field boundary element formulation for material nonlinear problems at finite strains

A boundary element formulation for geometrical nonlinear problems is presented, which is applicable for arbitrary constitutive equations based on the concept of hyperelastic response relative to an intermediate configuration. This includes purely hyperelastic problems at large elastic strains. In contrast to other formulations, the Total-Lagrange framework employed in this work significantly increases the numerical efficiency as the system matrices remain constant during the incremental solution and have to be computed only once. A nonlinear set of equations with an identical structure for both boundary and internal unknowns is derived. The basic unknowns are displacement gradients, which are calculated via integral equations and not by differentiation of the shape functions. The formulation can be consistently linearised to allow for the implementation of efficient iteration schemes using gradients, e.g. the Newton-Raphson scheme.

Analysis and sensitivity analysis by computer algebra for a third-order plate finite element

It is shown that even a complicated 50 degree of freedom laminated plate element can be dealt with analytically without numerical integration. In addition to saving computer time, this has many advantages. The different aspects of the element behaviour, i.e. material dependence, orientational dependence and element geometry are separated by using the basic element matrices of the finite element method. This allows for simple sensitivity analysis in optimal design solutions and also simplifies the solution of material non-linear problems.

ODE conversion techniques and their applications in computational mechanics

In this paper, a number of ordinary differential equation (ODE) conversion techniques for transformation of nonstandard ODE boundary value problems into standard forms are summarised, together with their applications to a variety of boundary value problems in computational solid mechanics, such as eigenvalue problem, geometrical and material nonlinear problem, elastic contact problem and optimal design problems through some simple and representative examples. The advantage of such approach is that various ODE boundary value problems in computational mechanics can be solved effectively in a unified manner by invoking a standard ODE solver.

ANALYSIS OF TRUSSES WITH NONLINEAR MATERIALS BY USING ENERGY PRINCIPLES AND SEQUENTIAL QUADRATIC PROGRAMMING

New analytical methods for trusses with nonlinear materials are presented by using energy principles and sequential quadratic programming (SQP) algorithms. The analytical problem of nonlinear truss is formulated as the total potential or complementary energy minimization problem and minimized with respect to the displacements of panel points or member forces respectively by using modified SOP algorithms. The formulations of the energy methods are quite simple and the methods can be applicable for any types of nonlinear material problems. Computational results for 3-31 bar statically indeterminate trusses with several types of nonlinear materials show that convergency and reliability of the method based on the complementary energy minimization is most excellent and the final results of nonlinear truss analyses can be obtained less than 2/3-1/3 of computational efforts compared with the incremental load method.

An energy balancing strategy for solution of combined geometrical and material nonlinearity problems

This paper describes an energy based line-search technique for large displacement and nonlinear stability analysis of planar truss and frame structures which, in addition to geometric non-linearities, simultaneously exhibit nonlinear material behavior. To improve the convergence characteristics of incremental-iterative procedures, a line search seeks a scalar factor which, at fixed load level, scales the displacement vector in such a way that the fundamental energy identity is satisfied. Furthermore, this factor can also be used for guiding the load incrementation. Aiming at computational simplicity and economy, efficient “section-type” beam elements are introduced. Using the total Lagrangian formulation, consideration of geometric nonlinearities yields, however, stiffness matrices which are linear and quadratic functions of the displacements. The material nonlinearity is treated by bilinear laws. The inelastic behavior is defined for several cross sections: thus, by forming the element stiffness matrices for bending the resulting variable stiffness must be accounted for. The effectiveness of the simple solution procedure has been tested using planar truss, beam, and cable-beam-type structures with known analytical and/or alternative solutions. Good agreement with these existing solutions demonstrates the applicability of the proposed method for routine engineering analysis.

Adaptive substructuring techniques in elasto-plastic finite element analysis

The application of substructuring techniques to the analysis of localized material nonlinear problems has been known for years. To substructure before starting nonlinear analysis, the analyst must know the locations and sizes of the possible plastic regions in advance. Should plastification occur in the linear substructures the analysis must stop; otherwise, inaccurate results are obtained. These difficulties can be eliminated by adaptive substructing techniques. In adaptive substructure analysis, the nonlinear substructure grows when the plastic zone expands or new plastification occurs in different places. This paper describes both interactive- and self-adaptive substructuring.

A Combined Finite Element—Transfer Matrix Method

The combined finite element‐transfer matrix method is applied to elastic‐plastic problems with large displacements. In the calculation program developed in this paper, the same procedures as those used in the finite element method based on load increment, are applied except for the estimation of approximate displacements for each specified incremental load. The Prandtl‐Reuss'law obeying the von Mises yield criterion is assumed, and a set of moving coordinate systems is used to take geometric nonlinearity into consideration. Various numerical examples of the geometric and material nonlinear problem are shown to demonstrate the accuracy of this method. These examples' results are in good agreement with those obtained by the finite element method and others.

Formulation methods of geometric and material nonlinearity problems

AbstractA concise survey of formulation methods of geometric and material nonlinearity problems is given. Differences between existing formulations in the literature are discussed. A consistent Lagrangian and updated Lagrangian formulations are derived from the energy balance equation transformed to the proper reference configuration. Differences between the existing formulations and similar ones in the literature are found to be in specific geometric nonlinear terms in the final incremental equation as well as in the definition of the load increment vector. Specific forms of constitutive equations for elastic and elastoplastic materials are presented. Some of the forms used by other authors in application to elastoplastic materials are shown to be inconsistent. Sample numerical examples intended for checking some particular points in the formulation are presented.