A Finite Element Technique for Limit Analysis of Structures

1990 ◽  
Vol 112 (2) ◽  
pp. 138-144 ◽  
Author(s):  
E. G. Berak ◽  
J. C. Gerdeen
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Limit Analysis ◽  
Variational Principles ◽  
Yield Criterion ◽  
Iteration Process ◽  
Limit Load ◽  
Upper And Lower Bounds ◽  
Algebraic Equations ◽  
Linear Algebraic Equations

Limit analysis provides an alternative to incremental elastic-plastic analysis for determining a limit load. The limit load is obtained from the lower and upper-bound theorems. These theorems, which are based on variational principles, establish the static and kinematic methods, respectively, and are particularly attractive for finite element implementation. A finite element approach using the definition of the p-norm is developed for calculating upper and lower bounds of the limit load multiplier for two-dimensional, rigid perfectly plastic structures which obey the von Mises yield criterion. Displacement and equilibrium building block quadrilateral elements are used in these dual upper and lower-bound formulations, respectively. The nonlinear finite element equations are transformed into systems of linear algebraic equations during the iteration process, and the solution vectors are determined using a frontal equation solver. The upper and lower-bound solutions are obtained in a reasonable number of iteration steps, and provide a good estimate of the limit load multiplier. Numerical results are provided to demonstrate this finite element procedure. In addition, this procedure is particularly applicable to the solution of complex problems using parallel processing on a supercomputer.

Efficient Tubesheet Design Using Repeated Elastic Limit Analysis Technique

2000 ◽  
Vol 123 (2) ◽  
pp. 197-202 ◽  
Author(s):  
W. D. Reinhardt ◽  
S. P. Mangalaramanan
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Lower Bound ◽  
Limit Analysis ◽  
Yield Criterion ◽  
Elastic Analysis ◽  
Collapse Load ◽  
Element Analysis ◽  
Simple Method ◽  
Yield Criteria

Conventional analysis of tubesheets in nuclear steam generators involves elastic analysis of a solid plate with equivalent properties. It has recently been recognized that alternate design techniques such as inelastic finite element analysis would lead to substantial cost reductions in material and manufacturing. Due to the anisotropy, arriving at yield criteria for an equivalent solid tubesheet is more complicated than for an isotropic solid. In addition, applying plastic finite element analysis in design is significantly more complex and time-consuming than elastic analysis. This paper proposes a relatively simple method to perform tubesheet collapse analysis. An anisotropic yield criterion is applied in conjunction with the classical lower-bound theorem of limit analysis and repeated elastic analyses involving elastic modulus modification. Two yield criteria are examined, namely Hill’s yield criterion and a recently suggested compressible fourth-order yield function. The collapse load predictions of the lower-bound equivalent solid methods are compared with the elastic-plastic finite element collapse load of the equivalent solid and of the actual perforated tubesheet.

A Numerical Approach for Lower Bound Limit Analysis

2014 ◽  
Vol 626 ◽  
pp. 474-481
Author(s):  
Ying Hua Liu ◽  
Bing Ye Xu ◽  
Xian He Du
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Limit Analysis ◽  
Yield Criterion ◽  
Numerical Procedure ◽  
Mathematical Programming Problem ◽  
Plastic Limit ◽  
Active Constraint ◽  
Plastic Limit Analysis ◽  
Lower Bound Limit Analysis

In this paper, a numerical procedure for plastic limit analysis of 3-D elastic-perfectly plastic bodies under complex loads is presented. The method is based on the lower-bound limit theorem and von Mises yield criterion so that the lower-bound limit analysis can be conducted by solving a nonlinear mathematical programming problem. A SQP algorithm and a dimension reduction-based technique are used to solve the discretized finite element optimization formulation. A conception of active constraint set is introduced, so that the number of constraints can be reduced greatly. The basis vectors of reduced residual stress spaces are constructed by performing an equilibrium iteration procedure of elasto-plastic finite element analysis. The numerical procedure is applied to carry out the plastic limit analysis of pipelines with part-through slots under internal pressure, bending moment and axial force. The effects of different sizes of part-through slots on the limit loads of pipelines are studied.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

Estimate of the Ultimate Load on Structural Members Subjected to Lateral Loads

2001 ◽  
Vol 38 (03) ◽  
pp. 169-176
Author(s):  
L. Belenkiy ◽  
Y. Raskin
Keyword(s):  
Finite Element ◽  
Limit Analysis ◽  
Ultimate Load ◽  
Limit Load ◽  
Plastic Behavior ◽  
Lateral Loads ◽  
Ship Structures ◽  
Strength Assessment ◽  
Stiffened Panels ◽  
Plate Elements

This paper examines plastic behavior of typical ship structures, specifically beams, grillages, and plates subjected to predominantly lateral loads. The ultimate loads, determined on the basis of the theorems of limit analysis [1,2], are evaluated using nonlinear finite-element plastic analysis. The relationships between analytical and finite-element models for prediction of ultimate loads of beams, stiffened panels, and grillages are illustrated. It has been shown that the ultimate loads, obtained from the theorems of limit analysis, can be successfully used for strength assessment of stiffened ship structures subjected to lateral loads. The effect of shear force on ultimate load is analyzed using the finite-element method. This paper confirms that in the case of beams and grillages under lateral loading, the ultimate load may characterize the threshold of the load at which a stiffened ship's structure fails by the development of excessive deflections. For plate elements, on the other hand, the plastic deflections represent the permissible limit of external load better than the ultimate limit load.

The ultimate pullout capacity of anchors in frictional soils

2006 ◽  
Vol 43 (8) ◽  
pp. 852-868 ◽  
Author(s):  
R S Merifield ◽  
S W Sloan
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Limit Analysis ◽  
Numerical Study ◽  
Past Research ◽  
Pullout Capacity ◽  
Current Design ◽  
Pullout Load ◽  
Ultimate Pullout Capacity ◽  
Frictional Soils

During the last 30 years various researchers have proposed approximate techniques to estimate the uplift capacity of soil anchors. As the majority of past research has been experimentally based, much current design practice is based on empiricism. Somewhat surprisingly, very few numerical analyses have been performed to determine the ultimate pullout loads of anchors. This paper presents the results of a rigorous numerical study to estimate the ultimate pullout load for vertical and horizontal plate anchors in frictional soils. Rigorous bounds have been obtained using two numerical procedures that are based on finite element formulations of the upper and lower bound theorems of limit analysis. For comparison purposes, numerical estimates of the break-out factor have also been obtained using the more conventional displacement finite element method. Results are presented in the familiar form of break-out factors based on various soil strength profiles and geometries and are compared with existing numerical and empirical solutions.Key words: anchor, pullout capacity, finite elements, limit analysis, lower bound, sand.

Accelerated Limit Loads Using Repeated Elastic Finite Element Analyses

2003 ◽  
Author(s):  
Prasad Mangalaramanan
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Limit Load ◽  
Finite Element Analyses ◽  
Limit Loads ◽  
Bound Theorem

This paper demonstrates the limitations of repeated elastic finite element analyses (REFEA) based limit load determination that uses the classical lower bound theorem. The r-node method is prescribed as an alternative for obtaining better limit load estimates. Lower bound aspects pertaining to r-nodes are also discussed.

Schwarz Type Solvers for -FEM Discretizations of Mixed Problems

2012 ◽  
Vol 12 (4) ◽  
pp. 369-390
Author(s):  
Sven Beuchler ◽  
Martin Purrucker
Keyword(s):  
Finite Element ◽  
Stokes Problem ◽  
Schur Complement ◽  
Algebraic Equations ◽  
The Finite Element Method ◽  
Contraction Ratio ◽  
Linear Algebraic Equations ◽  
Stokes Problems ◽  
Elasticity Problems ◽  
Element Pair

AbstractThis paper investigates the discretization of mixed variational formulation as, e.g., the Stokes problem by means of the hp-version of the finite element method. The system of linear algebraic equations is solved by the preconditioned Bramble-Pasciak conjugate gradient method. The development of an efficient preconditioner requires three ingredients, a preconditioner related to the components of the velocity modes, a preconditioner for the Schur complement related to the components of the pressure modes and a discrezation by a stable finite element pair which satisfies the discrete inf-sup-condition. The last condition is also important in order to obtain a stable discretization scheme. The preconditioner for the velocity modes is adapted from fast $hp$-FEM preconditioners for the potential equation. Moreover, we will prove that the preconditioner for the Schur complement can be chosen as a diagonal matrix if the pressure is discretized by discontinuous finite elements. We will prove that the system of linear algebraic equations can be solved in almost optimal complexity. This yields quasioptimal hp-FEM solvers for the Stokes problems and the linear elasticity problems. The latter are robust with respect to the contraction ratio ν. The efficiency of the presented solver is shown in several numerical examples.

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