The Equilibrium Cell-Based Smooth Finite Element Method for Shakedown Analysis of Structures

2019 ◽  
Vol 16 (05) ◽  
pp. 1840013 ◽  
Author(s):  
P. L. H. Ho ◽  
C. V. Le ◽  
T. Q. Chu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optimization Problem ◽  
Conic Programming ◽  
Equilibrium Equations ◽  
Shakedown Analysis ◽  
Numerical Examples ◽  
Elastic Stresses ◽  
Gauss Points ◽  
Element Method

This paper presents a novel equilibrium formulation, that uses the cell-based smoothed method and conic programming, for limit and shakedown analysis of structures. The virtual strains are computed using straining cell-based smoothing technique based on elements of discretized mesh. Fictitious elastic stresses are also determined within the framework of finite element method (CS-FEM)-based Galerkin procedure, and equilibrium equations for residual stresses are satisfied in an average sense at every cell-based smoothing cell. All constrains are imposed at only one point in the smoothing domains, instead of Gauss points as in a standard FEM-based procedure. The resulting optimization problem is then handled using the highly efficient solvers. Various numerical examples are investigated, and obtained solutions are compared with available results in the literature.

Hot Forging Comparative Analyses by Using a Combined Finite Element Method

2007 ◽  
Vol 340-341 ◽  
pp. 737-742
Author(s):  
Yong Ming Guo
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Hot Forging ◽  
Rigid Plastic ◽  
Numerical Examples ◽  
Comparative Analyses ◽  
Single Action ◽  
Element Method

In this paper, single action die and double action die hot forging problems are analyzed by a combined FEM, which consists of the volumetrically elastic and deviatorically rigid-plastic FEM and the heat transfer FEM. The volumetrically elastic and deviatorically rigid-plastic FEM has some merits in comparison with the conventional rigid-plastic FEMs. Differences of calculated results for the two forging processes can be clearly seen in this paper. It is also verified that these calculated results are similar to those of the conventional rigid-plastic FEM in comparison with analyses of the same numerical examples by the penalty rigid-plastic FEM.

scholarly journals A high order immersed finite element method for parabolic interface problems

2019 ◽  
Vol 29 ◽  
pp. 01007
Author(s):  
Derrick Jones ◽  
Xu Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Order ◽  
Interface Problems ◽  
Numerical Schemes ◽  
Numerical Examples ◽  
Immersed Finite Element Method ◽  
Immersed Finite Element ◽  
Time Marching ◽  
Element Method

We present a high order immersed finite element (IFE) method for solving 1D parabolic interface problems. These methods allow the solution mesh to be independent of the interface. Time marching schemes including Backward-Eulerand Crank-Nicolson methods are implemented to fully discretize the system. Numerical examples are provided to test the performance of our numerical schemes.

scholarly journals Stress evaluation in displacement-based 2D nonlocal finite element method

2018 ◽  
Vol 5 (1) ◽  
pp. 136-145 ◽  
Author(s):  
Aurora Angela Pisano ◽  
Paolo Fuschi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Field ◽  
Nonlocal Elasticity ◽  
Integration Technique ◽  
Stress Evaluation ◽  
Numerical Examples ◽  
Spurious Oscillations ◽  
Displacement Based ◽  
Element Method

Abstract The evaluation of the stress field within a nonlocal version of the displacement-based finite element method is addressed. With the aid of two numerical examples it is shown as some spurious oscillations of the computed nonlocal stresses arise at sections (or zones) of macroscopic inhomogeneity of the examined structures. It is also shown how the above drawback, which renders the stress numerical solution unreliable, can be viewed as the so-called locking in FEM, a subject debated in the early seventies. It is proved that a well known remedy for locking, i.e. the reduced integration technique, can be successfully applied also in the nonlocal elasticity context.

Error Bounds in an Optimization Problem Using the Finite-Element Method

1973 ◽  
Vol 40 (1) ◽  
pp. 204-208
Author(s):  
R. W. McLay ◽  
E. M. Buturla
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Bounds ◽  
Optimization Problem ◽  
Finite Element Solution ◽  
Element Solution ◽  
The Finite Element Method ◽  
The Relationship ◽  
Circular Disks ◽  
Element Method

An optimization problem involving the thermal deflections of two parallel circular disks is examined. Error bounds are developed for both the finite-element solution and the optimization problem. The relationship between the errors is illustrated in a single bound.

On the Unsymmetric Eigenproblem for the Buckling of Shells Under Pressure Loading

1983 ◽  
Vol 50 (1) ◽  
pp. 95-100 ◽  
Author(s):  
H. A. Mang ◽  
R. H. Gallagher
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hydrostatic Pressure ◽  
Stiffness Matrix ◽  
Circular Cylindrical Shell ◽  
The Finite Element Method ◽  
Equilibrium Equations ◽  
Buckling Loads ◽  
Large Rotations ◽  
Element Method

Consideration of the dependence of hydrostatic pressure on the displacements may result in significant changes of calculated buckling loads of thin arches and shells in comparison with loads calculated without consideration of this effect. The finite element method has made it possible to quantify these changes. On the basis of a shell theory of small displacements but moderately large rotations, this paper derives consistent incremental equilibrium equations for tracing, via the finite element method, the load-displacement path for thin shells subjected to nonuniform hydrostatic pressure and establishes the buckling condition from the incremental equilibrium equations. Within the framework of the finite element method, the character of hydrostatic pressure as one of a follower load is represented in the so-called pressure-stiffness matrix. For shells with loaded free edges, this matrix is unsymmetric. The principal objective of the present paper is to demonstrate that symmetrization of the pressure stiffness matrix resulting from linearization of the buckling condition yields buckling loads that are identical to the eigenvalues resulting from first-order perturbation analysis of the unsymmetric eigenproblem. A circular cylindrical shell with a free and a hinged end, subjected to hydrostatic pressure, is used as an example of the admissibility of symmetrizing the pressure stiffness matrix and for assessing its effect.

scholarly journals Two Algorithms for a Class of Elliptic Problems in Shape Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Li Tian ◽  
Dai Xiaoxia ◽  
Zhang Chengwei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optimal Design ◽  
Shape Optimization ◽  
Variational Problem ◽  
Optimization Problem ◽  
Elliptic Boundary ◽  
The Finite Element Method ◽  
Numerical Examples ◽  
Elliptic Boundary Value

We propose two algorithms for elliptic boundary value problems in shape optimization. With the finite element method, the optimization problem is replaced by a discrete variational problem. We give rules and use them to decide which elements are to be reserved. Those rules are determined by the optimization; as a result, we get the optimal design in shape. Numerical examples are provided to show the effectiveness of our algorithms.

Shakedown Analysis of Offshore Platform Under Varied Combined Loading

2011 ◽  
Author(s):  
Qiyi Zhang ◽  
Sheng Dong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Bearing Capacity ◽  
Ultimate Bearing Capacity ◽  
Offshore Platform ◽  
Static Equilibrium ◽  
Combined Loading ◽  
Shakedown Analysis ◽  
Elastic Plastic ◽  
Element Method

Based on static Melan shakedown theorem, an elastic-plastic finite element method is presented to analyze the shakedown of saturated undrained foundation due to varied combined loadings, and the shakedown loadings under different patterns of loading combination are compared. At the same time, a comparison is given between the shakedown failure envelop under varied combined loading and the failure envelop of ultimate bearing capacity under static equilibrium, and it is found that the shakedown loading under varied combined loading is less than the ultimate bearing capacity under combined loading.

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