Limit Loads Using Extended Variational Concepts in Plasticity

2000 ◽  
Vol 122 (3) ◽  
pp. 379-385
Author(s):  
R. Seshadri
Keyword(s):  
Lower Bound ◽  
Classical Method ◽  
Yield Criterion ◽  
Limit Load ◽  
Quadratic Equation ◽  
Limit Loads ◽  
Linear Elastic ◽  
Primary Stress ◽  
Component Design ◽  
Calculated Stress

Lower-bound limit load estimates are relevant from a standpoint of pressure component design, and are acceptable quantities for ascertaining primary stress limits. Elastic modulus adjustment procedures, used in conjunction with linear elastic finite element analyses, generate both statically admissible stress distributions and kinematically admissible strain distributions. Mura’s variational formulation for determining limit loads, originally developed as an alternative to the classical method, is extended further by allowing the elastic calculated stress fields to exceed yield provided they satisfy the “integral mean of yield” criterion. Consequently, improved lower-bound values for limit loads are obtained by solving a simple quadratic equation. The improved lower-bound limit load determination procedure, which is designated “the mα method,” is applied to symmetric as well as nonsymmetric components. [S0094-9930(00)01103-3]

Local Limit-Load Analysis Using the mβ Method

2006 ◽  
Vol 129 (2) ◽  
pp. 296-305 ◽  
Author(s):  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Local Limit ◽  
Limit Load ◽  
Element Analysis ◽  
Limit Loads ◽  
Linear Elastic ◽  
Reference Volume ◽  
Component Design ◽  
Load Analysis

Several upper-bound limit-load multipliers based on elastic modulus adjustment procedures converge to the lowest upper-bound value after several linear elastic iterations. However, pressure component design requires the use of lower-bound multipliers. Local limit loads are obtained in this paper by invoking the concept of “reference volume” in conjunction with the mβ multiplier method. The lower-bound limit loads obtained compare well to inelastic finite element analysis results for several pressure component configurations.

Integral Mean of Yield Criterion in Design and Fitness for Service Assessment

2008 ◽  
Author(s):  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Lower Bound ◽  
Variational Formulation ◽  
Yield Criterion ◽  
Hot Spot ◽  
Corrosion Damage ◽  
Limit Load ◽  
Assessment Procedure ◽  
Limit Loads ◽  
Reference Volume ◽  
Volume Method

Mura’s variational formulation for determining limit loads, originally developed as an alternative to classical methods, is extended further by allowing the pseudo-elastic distributions of stresses to lie outside the yield surface provided they satisfy the “integral mean of yield” criterion. Consequently, improved lower-bound and upper-bound values for limit loads are obtained. The mα estimation limit load method, reference volume method and the fitness for service assessment procedure (including corrosion damage and thermal hot spot damage), are all applications and extensions of the “integral mean of yield” criterion.

Estimating Lower Bound Limit Loads for Structures Subjected to Multiple Loads

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
C. Hari Manoj Simha ◽  
Reza Adibi-Asl
Keyword(s):  
Lower Bound ◽  
Elastic Stress ◽  
Limit Load ◽  
Selection Method ◽  
Elastic Analysis ◽  
Limit Loads ◽  
Linear Elastic ◽  
Multiple Loads ◽  
Cracked Structures ◽  
Appl Math

It is shown that the extended variational theorem of Mura et al. (1965, “Extended Theorems of Limit Analysis,” Q. Appl. Math., 23(2), pp. 171–179) can be applied to structures subjected to more than one load and be used to compute lower bound limit load multipliers. In particular, the multiplier proposed by Simha and Adibi-Asl (2011, “Lower Bound Limit Load Estimation Using a Linear Elastic Analysis,” ASME J. Pressure Vessel Technol., 134(2), p. 021207), which can be computed using an elastic stress field, is shown to be a lower bound. Furthermore, it is demonstrated that lower bound limit load for cracked structures may also be computed using a subvolume selection method. No iterations or elastic modulus adjustment are required. Several analytical and numerical examples that illustrate the procedure are presented.

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.

Incorporation of Strain Hardening Effect Into Simplified Limit Analysis

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
P. S. Reddy Gudimetla ◽  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Lower Bound ◽  
Strain Hardening ◽  
Limit Load ◽  
Element Analysis ◽  
Active Volume ◽  
Limit Loads ◽  
Reference Volume ◽  
Perfectly Plastic ◽  
Tangent Method ◽  
Elastic Perfectly Plastic

In this paper, a method for determining limit loads in the components or structures by incorporating strain hardening effects is presented. This has been done by including a certain amount of the strain hardening into limit load analysis, which normally idealizes the material to be elastic perfectly plastic. Typical strain hardening curves such as bilinear hardening and Ramberg–Osgood material models are investigated. This paper also focuses on the plastic reference volume correction concept to determine the active volume participating in plastic collapse. The reference volume concept in combination with mα-tangent method is used to estimate lower-bound limit loads of different components. Lower-bound limit loads obtained compare well with the nonlinear finite element analysis results for several typical configurations with/without crack.

Limit Analyisis of Frame Structure Based on the Elastic Modulus Reduction Method

2014 ◽  
Vol 578-579 ◽  
pp. 950-953
Author(s):  
Qiu Hua Duan ◽  
Yan Qing Guo ◽  
Dan Dan Zeng ◽  
Yue Jing Luo
Keyword(s):  
Elastic Modulus ◽  
Reduction Method ◽  
Yield Criterion ◽  
Bending Moment ◽  
Limit Load ◽  
Frame Structure ◽  
Structure Damage ◽  
Linear Elastic ◽  
Element Bearing ◽  
Modulus Reduction

An efficient linear elastic iterative finite element method, namely, the elastic modulus reduction method is introduced to calculate limit load of frame structure. The elastic modulus reduction method defines the element bearing ratio on the basis of the generalized yield criterion and the strain energy equilibrium principle. Because the bending moment is the main factor inducing the frame structure damage, the element bearing ratio only considering the bending moment yield is proposed. Numerical examples demonstrate the applicability and precision of the elastic modulus reduction method for limit analysis of frame structures.

scholarly journals Inf–sup conditions on convex cones and applications to limit load analysis

2019 ◽  
Vol 24 (10) ◽  
pp. 3331-3353 ◽  
Author(s):  
Jaroslav Haslinger ◽  
Stanislav Sysala ◽  
Sergey Repin
Keyword(s):  
Yield Criterion ◽  
Failure Mechanisms ◽  
Limit Load ◽  
Convex Cones ◽  
Mesh Adaptivity ◽  
Limit Loads ◽  
Perfectly Plastic ◽  
Dual Cones ◽  
Geotechnical Stability ◽  
Load Analysis

The paper is devoted to a family of specific inf–sup conditions generated by tensor-valued functions on convex cones. First, we discuss the validity of such conditions and estimate the value of the respective constant. Then, the results are used to derive estimates of the distance to dual cones, which are required in the analysis of limit loads of perfectly plastic structures. The equivalence between the static and kinematic approaches to limit analysis is proven and computable majorants of the limit load are derived. Particular interest is paid to the Drucker–Prager yield criterion. The last section exposes a collection of numerical examples including basic geotechnical stability problems. The majorants of the limit load are computed and expected failure mechanisms of structures are visualized using local mesh adaptivity.

Limit Load Estimation Using Plastic Flow Parameter in Repeated Elastic Finite Element Analyses

2002 ◽  
Vol 124 (4) ◽  
pp. 433-439 ◽  
Author(s):  
L. Pan ◽  
R. Seshadri
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Plastic Flow ◽  
Flow Parameter ◽  
Limit State ◽  
Limit Load ◽  
Finite Element Analyses ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Linear Elastic

The procedures described in this paper for determining a limit load is based on Mura’s extended variational formulation. Used in conjunction with linear elastic finite element analyses, the approach provides a robust method to estimate limit loads of mechanical components and structures. The secant modulus of the various elements in a finite element discretization scheme is prescribed in order to simulate the distributed effect of the plastic flow parameter, μ0. The upper and lower-bound multipliers m0 and m′ obtained using this formulation converge to near exact values. By using the notion of “leap-frogging” to limit state, an improved lower-bound multiplier, mα, can be obtained. The condition for which mα is a reasonable lower bound is discussed in this paper. The method is applied to component configurations such as cylinder, torispherical head, indeterminate beam, and a cracked specimen.

Limit Load Estimate Using Reference Volume Approach

2010 ◽  
Author(s):  
P. S. Reddy Gudimetla ◽  
R. Seshadri ◽  
Munaswamy Katna
Keyword(s):  
Lower Bound ◽  
Limit Load ◽  
Limit Loads ◽  
Volume Correction ◽  
Reference Volume ◽  
Tangent Method ◽  
Novel Methods ◽  
Volume Method ◽  
General Component

In this paper two novel methods (elastic reference volume method and plastic reference volume method) for reference volume correction while finding out limit loads in the components or structures are presented. These reference volume correction concepts are used in combination with mα-Tangent method to obtain the lower bound limit load of general component or structure.

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