The sensitivity analysis of the drawpiece response on the material model parameters

On this paper the numerical analysis of the drawing process with use the Finite Element Method is presented. The sensitivity of stresses field on the edge and the round edge of drawpiece on the tangent modulus and yield stress is defined. The analysis with the explicit method in the ANSYS LS-Dyna system is passed. The Die and the stamp as not deformable bodies are accepted and with the shell finite elements are discretized. The drawpiece with the solid finite elements are discretized. Sample results of computer simulations are presented. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sizing and shape design sensitivity analysis using a hybrid finite element code

A numerical implementation of sizing and shape design sensitivity analysis of structural systems is presented, using the versatility and convenience of an existing finite element structural analysis code and its database management system. The finite element code used in the implementation presented is the Engineering Analysis Language (EAL), which is based on a hybrid method of analysis. Design sensitivity computations are carried out using the database management system of EAL, without writing a separate program and a separate database. Accurate design sensitivity results are obtained without the uncertainty of numerical accuracy associated with selection of finite difference perturbations. Sizing design parameters, such as crossectional area of beams and thickness of plates, and shape design parameters are considered in this paper. Structural performance measures considered include displacement and stress.     

Shape sensitivity analysis in the extended finite element method

The contribution is concerned with the derivation and implementation of shape sensitivity analysis in the context of the extended finite element method (xfem). Here, the displacement approximation is enhanced in order to model strong and weak discontinuities along the interfaces and cracks. Consequently, sensitivity analysis must be accomplished for the extended formulation based on a sub-integration technique on sub-domains of the cut elements. This cumbersome and error-prone work can be circumvent using a standard treatment of sub-elements on an appropriately defined sub-mesh. These modifications guarantee exact analytical sensitivities even for distorted finite element domains. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An analysis of finite element locking in a parameter dependent model problem

Summary. We consider the bilinear finite element approximation of smooth solutions to a simple parameter dependent elliptic model problem, the problem of highly anisotropic heat conduction. We show that under favorable circumstances that depend on both the finite element mesh and on the type of boundary conditions, the effect of parametric locking of the standard FEM can be reduced by a simple variational crime. In our analysis we split the error in two orthogonal components, the approximation error and the consistency error, and obtain different bounds for these separate components. Also some numerical results are shown. Received September 6, 1999 / Revised version received March 28, 2000 / Published online April 5, 2001     

Optimization the shape of finite element in shot peening process

This paper contains modelling and numerical simulations of shot peening process. The application in Ansys/LS – Dyna programme were elaborated. The phenomena of shot peening process on a typical incremental step were described using a step-by-step incremental procedure, with an updated Lagrangian formulation.Finite elements methods (FEM) and the dynamic explicit method (DEM) were used to obtain the solution. The main purpose of this article is to determinate optimal model of shot peening process (convergence resulting for minimal number of finite elements and their optimal shapes). Examples of calculations were presented. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new method of sensitivity analysis of static responses for finite element systems

This paper is the continuation of Liang et al. J. Comput. Struct. 62 (2) (1997) 243–251. In this paper, a set of explicit formulations of variations for calculating sensitivity of static responses are presented. This method may greatly increase the computational efficiency if used with the M–P inverse topological variation method. By using this method the exact sensitivity can be obtained.     

The material parameter design and finite element simulation of the quadrilateral thermal cloak device

In this paper, we first design a coordinate transformation and derive the anisotropic material parameters of the quadrilateral thermal cloak according to the transformation thermodynamics principle. Then, since the derived parameters are inherently anisotropic, we eliminate its anisotropy by considering the effective medium theory and use a layered structure of metamaterials composed of only two isotropic materials to design the cloak device. Finally, we simulate the performance of a perfect and layered thermal cloak by the finite element method. To the best of our knowledge, this is the first work to design and simulate the performance of this quadrilateral thermal cloak by the finite element method(FEM).     

Peridynamics via finite element analysis

Peridynamics is a recently developed theory of solid mechanics that replaces the partial differential equations of the classical continuum theory with integral equations. Since the integral equations remain valid in the presence of discontinuities such as cracks, the method has the potential to model fracture and damage with great generality and without the complications of mathematical singularities that plague conventional continuum approaches. Although a discretized form of the peridynamic integral equations has been implemented in a meshless code called EMU, the objective of the present paper is to describe how the peridynamic model can also be implemented in a conventional finite element analysis (FEA) code using truss elements. Since FEA is arguably the most widely used tool for structural analysis, this implementation may hasten the verification of peridynamics and significantly broaden the range of problems that the practicing analyst might attempt. Also, the present work demonstrates that different subregions of a model can be solved with either the classical partial differential equations or the peridynamic equations in the same calculation thus combining the efficiency of FEA with the generality of peridynamics. Several example problems show the equivalency of the FEA and the meshless peridynamic approach as well as demonstrate the utility and robustness of the method for problems involving fracture, damage and penetration.     

Uncertainty finite element dynamic analysis

An inference-dynamic model is developed based on a model dynamic analysis using a moving boundary condition. The uncertainty of the physical parameters is implemented in the model using an inference scheme coupled with a perturbation technique. Finally, the first two statistical moments of the displacements and the stress field are estimated according to the proposed analytical scheme and are in good agreement with the initially assumed fields.     

Nonlinear,finite deformation,finite element analysis

The roles of the consistent Jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method, are emphasized in this paper, and demonstrated using the commercial software ABAQUS standard. In doing so, the necessity for correctly employing user material subroutines to solve nonlinear problems involving large deformation and/or large rotation is clarified. Starting with the rate form of the principle of virtual work, the derivations of the material tangent moduli, the consistent Jacobian matrix, the stress/strain measures, and the objective stress rates are discussed and clarified. The difference between the consistent Jacobian matrix (which, in the ABAQUS UMAT user material subroutine is referred to as DDSDDE) and the material tangent moduli (C^e) needed for the stress update is pointed out and emphasized in this paper. While the former is derived based on the Jaumann rate of the Kirchhoff stress, the latter is derived using the Jaumann rate of the Cauchy stress. Understanding the difference between these two objective stress rates is crucial for correctly implementing a constitutive model, especially a rate form constitutive relation, and for ensuring fast convergence. Specifically, the implementation requires the stresses to be updated correctly. For this, the strains must be computed directly from the deformation gradient and corresponding strain measure (for a total form model). Alternatively, the material tangent moduli derived from the corresponding Jaumann rate of the Cauchy stress of the constitutive relation (for a rate form model) should be used. Given that this requirement is satisfied, the consistent Jacobian matrix only influences the rate of convergence. Its derivation should be based on the Jaumann rate of the Kirchhoff stress to ensure fast convergence; however, the use of a different objective stress rate may also be possible. The error associated with energy conservation and work-conjugacy due to the use of the Jaumann objective stress rate in ABAQUS nonlinear incremental analysis is viewed as a consequence of the implementation of a constitutive model that violates these requirements.     

Shape sensitivity analysis of an elastic contact problem: Convergence of the Nitsche based finite element approximation

In a recent work, we introduced a finite element approximation for the shape optimization of an elastic structure in sliding contact with a rigid foundation where the contact condition (Signorini’s condition) is approximated by Nitsche’s method and the shape gradient is obtained via the adjoint state method. The motivation of this work is to propose an a priori convergence analysis of the numerical approximation of the variables of the shape gradient (displacement and adjoint state) and to show some numerical results in agreement with the theoretical ones. The main difficulty comes from the non-differentiability of the contact condition in the classical sense which requires the notion of conical differentiability.     

Criteria sensitivity analysis: a new approach to parameter sensitivity

The problem of parameter sensitivity is not well defined. This paper aims to make it well defined. This is done by requiring the modeller to provide a performance indicator l(X,t,β) which is a measure of how the behaviour of the system is to be judged. This forces the modeller to be precise about what he/she regards as acceptable behaviour. Mathematically we define behaviour to be acceptable at β if l >0 for that β, and we define the system as sensitive if the set of acceptable β's is small. The analysis which is required is termed criteria sensitivity analysis. This method is applicable to many different kinds of models. The basic ideas of criteria sensitivity analysis are presented here. A static model is used to demonstrate major points. The power of this new approach is illustrated by an application to a dynamic model.     

The finite element method used for determining impedance of symmetrical shape conductors carrying alternating current

The paper presents a general method of calculating the fields in the conductors of unknown boundary conditions upon their surface. The idea is to combine the Bubnov-Galerkin method in its numerical form with the separation of variables by means of the finite element method so that the analysis of skin effect in the conductors placed in homogeneous, isotropic medium is possible. The method was used for determining impedance of some selected polygonal and symmetrical shape conductors carrying alternating current. On the basis of numerical calculations, graphs of resistance and inner reactance were plotted.     

The application of parameter sensitivity analysis methods to inverse simulation models

Knowledge of the sensitivity of inverse solutions to variation of parameters of a model can be very useful in making engineering design decisions. This article describes how parameter sensitivity analysis can be carried out for inverse simulations generated through approximate transfer function inversion methods and also through the use of feedback principles. Emphasis is placed on the use of sensitivity models and the article includes examples and a case study involving a model of an underwater vehicle. It is shown that the use of sensitivity models can provide physical understanding of inverse simulation solutions that is not directly available using parameter sensitivity analysis methods that involve parameter perturbations and response differencing.     

Fuzzy finite element analysis for free vibration response of functionally graded semi-rigid frame structures

This study contributes a practical approach for the fuzzy free vibration quantification of functionally graded semi-rigid frame structures. A new Timoshenko beam element is formulated to include the connection rigidity for the analysis purpose. The finite element formulation is general to present different semi-rigid conditions, whereas hinged and rigid connections are special cases. Furthermore, an efficient response-surface-based fuzzy analysis is established based on the α–cut strategy and first-order Taylor's approximation to predict the fuzzy natural frequencies of the structures. Highlighted point is that various input uncertainties, such as the material characteristics, the member dimensions, and the connection rigidities, can be incorporated in the analysis by the presented fuzzy methodology. Computational efficiency and correctness of the proposed method are shown, and the effect of the uncertainties, especially of the connection rigidities, on the natural frequency of semi-rigid FGM structures is explored via solving some numerical examples.     

MIXED FINITE ELEMENT METHOD FOR THE CONVECTION-DOMINATED DIFFUSION PROBLEMS WITH SMALL PARAMETER ε

In rids paper a mixed finite element method for the convection-dominated diffusion problems with small parameter ε is presented,the effect of the parameter ε on the approximation error is considered and a sufficient condition for optimal error estimates is derived. The paper also shows that under some conditions,the standard finite dement method only gives a hounded solution,however the mixed finite element method gives a convergent one.     

A posteriori error estimation for finite element discretization of parameter identification problems

Summary. In this paper we develop an a posteriori error estimator for parameter identification problems. The state equation is given by a partial differential equation involving a finite number of unknown parameters. The presented error estimator aims to control the error in the parameters due to discretization by finite elements. For this, we consider the general setting of a partial differential equation written in weak form with abstract parameter dependence. Exploiting the special structure of the parameter identification problem, allows us to derive an error estimator which is cheap in comparison to the overall optimization algorithm. Several examples illustrating the behavior of an adaptive mesh refinement algorithm based on our error estimator are discussed in the numerical section. For the problems considered here, both, the efficiency of the estimator and the quality of the generated meshes are satisfactory. Mathematics Subject Classifications (2000): 65K10, 65N30, 49K20This work has been supported by the German Research Foundation (DFG) through SFB 359 Reactive Flow, Diffusion and Transport and Graduiertenkolleg Modellierung und wissenschaftliches Rechnen in Mathematik und Naturwissenschaften     

Nonlinear finite element analysis of concrete structures

This paper deals with three-dimensional nonlinear finite element analysis of concrete structures. A new three-parameter failure criterion, formulated in terms of three stress invariants, is suggested for plain concrete. The criterion can accurately describe available experimental data throughout the stress range from tensile stresses to high compressive stresses. The constitutive matrix of a cracked concrete element is deduced by coupling the normal and tangential effects of crack bands. The modeling of reinforcement and its interaction with concrete are also discussed. Numerical examples of plain and reinforced concrete are presented. The computational results compare satisfactorily with experimental data.This research is supported by the Chinese National Committee of Science and Technology and the Chinese National Bureau of Nuclear Safety.