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

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.

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Limit Loads for Layered Structures Using Extended Variational Principles and Repeated Elastic Finite Element Analysis

Journal of Pressure Vessel Technology ◽

10.1115/1.1498845 ◽

2002 ◽

Vol 124 (4) ◽

pp. 425-432 ◽

Cited By ~ 3

Author(s):

L. Pan ◽

R. Seshadri

Keyword(s):

Finite Element ◽

Flow Parameter ◽

Variational Principles ◽

Limit State ◽

Limit Load ◽

Layered Structures ◽

Element Analysis ◽

Element Discretization ◽

Limit Loads ◽

Strength Performance

Layered structures are used in industry due to their better cost-to-strength and weight-to-strength performance compared with conventional structures. This paper presents a simple and systematic procedure to estimate the limit load for those layered structures that can undergo plastic collapse. The extended Mura’s variational principle is used in conjunction with repeated elastic finite element analyses (FEA). The elastic parameters are modified in order to ensure that the repeated analyses lead to a stress distribution close to the limit state. The secant modulus of a given element within the finite element discretization scheme is employed to simulate the plastic flow parameter μ0, and rapid convergence of estimated multipliers to the exact value is achieved. By using the notion of “leap-frogging” to limit state, improved lower-bound values of limit loads have been obtained. The method has been applied to layered cylinders and beams.

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Accelerated Limit Loads Using Repeated Elastic Finite Element Analyses

Computer Technology and Applications ◽

10.1115/pvp2003-1890 ◽

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.

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Limit Analysis for Anisotropic Solids Using Variational Principle and Repeated Elastic Finite Element Analyses

Fitness for Service Evaluations and Non-Linear Analysis ◽

10.1115/pvp2002-1321 ◽

2002 ◽

Cited By ~ 2

Author(s):

L. Pan ◽

R. Seshadri

Keyword(s):

Finite Element ◽

Variational Principle ◽

Limit State ◽

Limit Load ◽

Anisotropic Materials ◽

Stress Fields ◽

Finite Element Analyses ◽

Structural Components ◽

Directionally Solidified ◽

Elastic Compensation Method

Many structural components, such as rolled sheets, directionally solidified superalloys and composites, are made of anisotropic materials. The knowledge of limit load is useful in the design and the sizing of these components and structures. This paper presents the extension of the modified mα-method to anisotropic materials. Mura’s variational principle is employed in conjunction with repeated elastic finite element analyses (FEA). The secant modulus of the discretized finite elements in the reference direction in successive elastic iterations is used to estimate the plastic flow parameter for the anisotropic components. The modified initial elastic properties are adopted to ensure the “elastic” stress fields satisfy the anisotropic yield surface. Using the notion of “leap-frogging” to limit state, improved lower-bound limit loads can be obtained. The formulation is applied to two anisotropic components, and the limit load estimates are compared with those using elastic compensation method and inelastic FEA.

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LIMIT LOADS OF FRAMED STRUCTURES AND ARCHES USING THE GLOSS R-NODE METHOD

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-1993-0012 ◽

1993 ◽

Vol 17 (2) ◽

pp. 197-214

Author(s):

C.P.D. Fernando ◽

R. Seshadri

Keyword(s):

Finite Element ◽

Approximate Method ◽

Equivalent Stress ◽

Limit Load ◽

Load Control ◽

Finite Element Analyses ◽

Limit Loads ◽

Framed Structures ◽

Linear Elastic ◽

Reference Stress

An approximate method for determining limit loads of mechanical components and structures on the basis of two linear elastic finite element analyses is described. The load-control nature of the redistribution nodes (r-nodes) leads to considerable simplifications. The combined r-node equivalent stress, which can be obtained by invoking an appropriate multibar mode, can be identified with the reference stress. The method is applied to beam, framed and arched structures, and the limit load estimates obtained are reasonably accurate.

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Simplified Limit Load Determination Using the mα-Tangent Method

Volume 2: Computer Applications/Technology and Bolted Joints ◽

10.1115/pvp2008-61171 ◽

2008 ◽

Author(s):

R. Seshadri ◽

M. M. Hossain

Keyword(s):

Finite Element ◽

Rapid Determination ◽

Limit Load ◽

Finite Element Analyses ◽

Element Analysis ◽

Limit Loads ◽

Linear Elastic ◽

Tangent Method ◽

Mechanical Components

Limit load determination of mechanical components and structures by the mα-tangent method is proposed herein. The proposed technique is a simplified method that enables rapid determination of limit loads for a general class of mechanical components and structures. The method makes use of statically admissible stress field based on a linear elastic finite element analysis to estimate the limit loads. The method is applied to a number of mechanical component configurations and the results compare well with those obtained by the corresponding elastic-plastic finite element analyses results.

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