Showing papers on "Finite element limit analysis published in 2015"

Extended Finite Element Method: Theory and Applications

Abstract: Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics • Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. • Covers numerous applications of XFEM including fracture mechanics, large deformation, plasticity, multiphase flow, hydraulic fracturing and contact problems • Accompanied by a website hosting source code and examples

An Introduction to Nonlinear Finite Element Analysis: with applications to heat transfer, fluid mechanics, and solid mechanics

Abstract: 1. General Introduction and Mathematical Preliminaries 2. Elements of Nonlinear Continuum Mechanics 3. The Finite Element Method: A Review 4. One-Dimensional Problems Involving a Single Variable 5. Nonlinear Bending of Straight Beams 6. Two-Dimensional Problems Involving a Single Variable 7. Nonlinear Bending of Elastic Plates 8. Nonlinear Bending of Elastic Shells 9. Finite Element Formulations of Solid Continua 10. Weak-Form Finite Element Models of Flows of Viscous Incompressible Fluids 11. Least-Squares Finite Element Models of Flows of Viscous Incompressible Fluids Appendix 1: Solution Procedures for Linear Equations Appendix 2: Solution Procedures for Nonlinear Equations

Finite difference/finite element method for a nonlinear time-fractional fourth-order reaction–diffusion problem

Abstract: In this article, a finite difference/finite element algorithm, which is based on a finite difference approximation in time direction and finite element method in spatial direction, is presented and discussed to cast about for the numerical solutions of a time-fractional fourth-order reaction–diffusion problem with a nonlinear reaction term. To avoid the use of higher-order elements, the original problem with spatial fourth-order derivative need to be changed into a second-order coupled system by introducing an intermediate variable σ = Δ u . Then the fully discrete finite element scheme is formulated by using a finite difference approximation for time fractional and integer derivatives and finite element method in spatial direction. The unconditionally stable result in the norm, which just depends on initial value and source item, is derived. Some a priori estimates of L 2 -norm with optimal order of convergence O ( Δ t 2 − α + h m + 1 ) , where Δ t and h are time step length and space mesh parameter, respectively, are obtained. To confirm the theoretical analysis, some numerical results are provided by our method.

Real-time control of soft-robots using asynchronous finite element modeling

Abstract: Finite Element analysis can provide accurate deformable models for soft-robots. However, using such models is very difficult in a real-time system of control. In this paper, we introduce a generic solution that enables a high-rate control and that is compatible with strong real-time constraints. From a Finite Element analysis, computed at low rate, an inverse model of the robot outputs the setpoint values for the actuator in order to obtain a desired trajectory. This inverse problem uses a QP (quadratic-programming) algorithm based on the equations set by the Finite Element Method. To improve the update rate performances, we propose an asynchronous simulation framework that provides a better trade-off between the deformation accuracy and the computational burden. Complex computations such as accurate FEM deformations are done at low frequency while the control is performed at high frequency with strong real-time constraints. The two simulation loops (high frequency and low frequency loops) are mechanically coupled in order to guarantee mechanical accuracy of the system over time. Finally, the validity of the multi-rate simulation is discussed based on measurements of the evolution in the QP matrix and an experimental validation is conducted to validate the correctness of the high-rate inverse model on a real robot.

Comparison of finite-element limit analysis and strength reduction techniques

Abstract: In practical geotechnical engineering the factor of safety is still determined by means of simple limit equilibrium analysis in many cases. However, because displacement finite-element analysis is routinely applied for assessing displacements and stresses for working load conditions, this technique is increasingly being used to calculate ultimate limit states and, consequently, factors of safety, usually by means of the so-called strength reduction technique, and results which are comparable to those obtained with limit equilibrium methods have been reported in the literature. However, owing to the inherent assumptions of limit equilibrium analyses, they do not always provide unique factors of safety. The purpose of this paper is on the one hand to compare the strength reduction method with rigorous limit analyses which are based on collapse theorems of plasticity, and on the other hand to investigate if a shortcoming of the strength reduction method, namely possible numerical instabilities for non-associ...

Finite Element Modeling

Abstract: This chapter covers the numerical modeling of carbon nanotubes based on the finite element method. The approach based on a three-dimensional space-frame structure where the bonds between carbon atoms are considered as connecting load-carrying generalized beam members, while the carbon atoms act as joints of the members, is introduced. The assignment of corresponding material and geometric properties is explained in detail.

Slope Stability Charts for Two-Layered Purely Cohesive Soils Based on Finite-Element Limit Analysis Methods

Abstract: Stability charts for soil slopes, first produced in the first half of the twentieth century, continue to be used extensively as design tools, and draw the attention of many investigators. This paper uses finite-element upper and lower bound limit analysis to assess the short-term stability of slopes in which the slope material and subgrade foundation material have two distinctly different undrained strengths. The stability charts are proposed, and the exact theoretical solutions are bracketed to within 4.2% or better. In addition, results from the limit-equilibrium method (LEM) have been used for comparison. Differences of up to 20% were found between the numerical limit analysis and LEM solutions. It also shown that the LEM sometimes leads to errors, although it is widely used in practice for slope stability assessments.

Undrained stability of dual square tunnels

Abstract: In this paper, finite element limit analysis (FELA) and semi-analytical rigid block techniques are used to investigate the influence of tunnel spacing on the undrained stability of two unlined square tunnels constructed side by side. The tunnels, which are assumed to be straight and infinitely long, are modelled under conditions of plane strain. Upper and lower bounds on the stability of the tunnels are obtained using FELA; the numerical formulation of which is based upon the bounds theorems of classical plasticity. These bounds, which bracket the true collapse load from above and below, are found to be in good agreement with one another. Rigid block methods also provided an upper bound estimate on tunnel stability which was generally higher than, but still in good agreement with, the FELA upper bound. Failure mechanisms associated with the collapse of the dual tunnels were investigated, and for deeper tunnels, it was found that mechanisms extend much deeper below the tunnels than the collapse mechanisms associated with a single tunnel. Results from this study are summarised in dimensionless stability charts for use by practitioners.

Strength reduction finite-element limit analysis

Abstract: A procedure for strength reduction analysis using finite-element limit analysis is presented. The scheme is completely general and does not require decision making regarding the loads needed to drive the system to failure. Rather, the scheme is based on the ability of modern interior-point methods to detect infeasibility in a controlled and reliable manner. The new scheme is illustrated by an example involving a strip footing on top of a slope.

Application of Semi-analytical Finite Element Method Coupled with Infinite Element for Analysis of Asphalt Pavement Structural Response

Abstract: A specific computational program SAFEM was developed based on semi-analytical finite element (FE) method for analysis of asphalt pavement structural responses under static loads. The reliability and efficiency of this FE program was proved by comparison with the general commercial FE software ABAQUS. In order to further reduce the computational time without decrease of the accuracy, the infinite element was added to this program. The results of the finite-infinite element coupling analysis were compared with those of finite element analysis derived from the verified FE program. The study shows that finite-infinite element coupling analysis has higher reliability and efficiency.

Finite Element Analysis for Contact Problems

Abstract: When two or more bodies collide, contact occurs between two surfaces of the bodies so that they cannot overlap in space. Metal formation, vehicle crash, projectile penetration, various seal designs, and bushing and gear systems are only a few examples of contact phenomena. This chapter is organized as follows. In Sect. 5.2, simple one-point contact examples are presented in order to show the characteristics of contact phenomena and possible solution strategies. In Sect. 5.3, a general formulation of contact is presented based on the variational formulation. Sect. 5.4 focuses on finite element discretization and numerical integration of the contact variational form. Three-dimensional contact formulation is presented in Sect. 5.5 . From the finite element point of view, all formulations involve use of some form of a constraint equation. Because of the highly nonlinear and discontinuous nature of contact problems, great care and trial-and-error are necessary to obtain solutions to practical problems. Section 5.6 presents modeling issues related to contact analysis, such as selecting slave and master bodies, removing rigid-body motions, etc.

On a Space-Time Extended Finite Element Method for the Solution of a Class of Two-Phase Mass Transport Problems

Abstract: In the present thesis a new numerical method for the simulation of mass transport in an incompressible immiscible two-phase flow system is presented. The mathematical model consists of convection diffusion equations on moving domains which are coupled through interface conditions. One of those conditions, the Henry interface condition, prescribes a jump discontinuity of the solution across the moving interface. For the description of the interface position and its evolution we consider interface capturing methods, for instance the level set method. In those methods the mesh is not aligned to the evolving interface such that the interface intersects mesh elements. Hence, the moving discontinuity is located within individual elements which makes the numerical treatment challenging. The discretization presented in this thesis is based on essentially three core components. The first component is an enrichment with an extended finite element (XFEM) space which provides the possibility to approximate discontinuous quantities accurately without the need for aligned meshes. This enrichment, however, does not respect the Henry interface condition. The second component cures this issue by imposing the interface condition in a weak sense into the discrete variational formulation of the finite element method. To this end a variant of the Nitsche technique is applied. For a stationary interface the combination of both techniques offers a good way to provide a reliable method for the simulation of mass transport in two-phase flows. However, the most difficult aspect of the problem is the fact that the interface is typically not stationary, but moving in time. The numerical treatment of the moving discontinuity requires special care. For this purpose a space-time variational formulation, the third core component of this thesis, is introduced and combined with the first two components: the XFEM enrichment and the Nitsche technique. In this thesis we present the components and the resulting methods one after another, for stationary and non-stationary interfaces. We analyze the methods with respect to accuracy and stability and discuss important properties. For the case of a stationary interface the combination of an XFEM enrichment and the Nitsche technique, the Nitsche-XFEM method, has been introduced by other authors. Their method, however, lacks stability in case of dominating

Drilling of metal matrix composites: Experimental and finite element analysis:

Abstract: Drilling is an indispensable machining operation, which is mostly performed for making holes in an intricate composite part. In this research investigation, a finite element model has been developed to simulate the drilling behavior of Al1100/10% SiC metal matrix composite using finite element platform (ABAQUS/Explicit). The effect of cutting speed and feed rate on thrust force has also been experimentally evaluated. It was found that the magnitude of thrust force obtained from the proposed finite element model is in close agreement with the experimental values. It was also established that the proposed finite element model is quite efficient to predict the thrust force signals generated during drilling of metal matrix composites.

Finite strain fracture analysis using the extended finite element method with new set of enrichment functions

Abstract: Summary Nonlinear fracture analysis of rubber-like materials is computationally challenging due to a number of complicated numerical problems. The aim of this paper is to study finite strain fracture problems based on appropriate enrichment functions within the extended finite element method. Two-dimensional static and quasi-static crack propagation problems are solved to demonstrate the efficiency of the proposed method. Complex mixed-mode problems under extreme large deformation regimes are solved to evaluate the performance of the proposed extended finite element analysis based on different tip enrichment functions. Finally, it is demonstrated that the logarithmic set of enrichment functions provides the most accurate and efficient solution for finite strain fracture analysis. Copyright © 2015 John Wiley & Sons, Ltd.