Lower Bound Limit Load Determination: The mβ-Multiplier Method

2004 ◽  
Vol 126 (2) ◽  
pp. 237-240 ◽  
Author(s):  
R. Seshadri ◽  
H. Indermohan
Keyword(s):  
Lower Bound ◽  
Equivalent Stress ◽  
Limit Load ◽  
Oscillatory Behavior ◽  
Multiplier Method ◽  
Linear Elastic ◽  
Maximum Equivalent Stress ◽  
Determination Methods ◽  
Distribution Of Stress ◽  
Limited Accuracy

The existing lower bound limit load determination methods, that are based on linear elastic analysis such as the classical and mα-multiplier methods, have a dependence on the maximum equivalent stress. These methods are therefore sensitive to localized plastic action, which occurs in components with thin or slender construction, or those containing notches and cracks. Sensitivity manifests itself as relatively poor lower bounds during the initial elastic iterations of the elastic modulus adjustment procedures, or oscillatory behavior of the multiplier during successive elastic iterations leading to limited accuracy. The mβ-multiplier method proposed in this paper starts out with Mura’s inequality that relates the upper bound to the exact multiplier by making use of the “integral mean of yield.” The formulation relies on a “reference parameter” that is obtained from considering a distribution of stress rather than a single maximum equivalent stress. As a result, good limit load estimates have been obtained for several pressure component configurations.

Lower Bound Limit Load Determination: The mβ-Multiplier Method

2003 ◽  
Author(s):  
R. Seshadri ◽  
H. Indermohan
Keyword(s):  
Lower Bound ◽  
Equivalent Stress ◽  
Limit Load ◽  
Oscillatory Behavior ◽  
Multiplier Method ◽  
Linear Elastic ◽  
Maximum Equivalent Stress ◽  
Determination Methods ◽  
Distribution Of Stress ◽  
Limited Accuracy

The existing lower bound limit load determination methods that are based on linear elastic analysis such as the classical and mα-multiplier methods have a dependence on the maximum equivalent stress. These methods are therefore sensitive to localized plastic action, which occurs in components with thin or slender construction, or those containing notches and cracks. Sensitivity manifests itself as relatively poor lower bounds during the initial elastic iterations of the elastic modulus adjustment procedures, or oscillatory behavior of the multiplier during successive elastic iterations leading to limited accuracy. The mβ-multiplier method proposed in this paper starts out with Mura’s inequality that relates the upper bound to the exact multiplier by making use of the “integral mean of yield.” The formulation relies on a “reference parameter” that is obtained by considering a distribution of stress rather than a single maximum equivalent stress. As a result, good limit load estimates have been obtained for several pressure component configurations.

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.

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.

Study on the Strength of Axial Fan Blades Based on Fluid-Solid Coupling

2013 ◽  
Vol 448-453 ◽  
pp. 3382-3385
Author(s):  
Song Ling Wang ◽  
Shou Fang Liang ◽  
Bin Hu ◽  
Lei Zhang
Keyword(s):  
Flow Field ◽  
Field Data ◽  
Equivalent Stress ◽  
Aerodynamic Load ◽  
Total Deformation ◽  
Axial Fan ◽  
Static Structure ◽  
Maximum Deformation ◽  
Maximum Equivalent Stress ◽  
Distribution Of Stress

Based on one-way fluid-solid coupling, a variable pitch axial fan was simulated through ANSYSY Workbench platform. With the software Fluent to describe the flow field and the software Mechanical to describe the structure field, the static structure analysis of the blades was carried out to study the strength of the blades. The flow field data were applied on the blades by interpolation. The results show that the centrifugal force plays an important role on the strength characteristics of the blades. Considering the aerodynamic load, the distribution of stress of the blades tends to be more uneven, the maximum equivalent stress reduces by 4.5% and the maximum deformation decreases by 26.6%. With the increase of flow, the maximum equivalent stress and the maximum total deformation of the blades decrease gradually.

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.

Analysis of Sealing Ability of Premium Tubing Connection under Axial Alternating Tension Load

2013 ◽  
Vol 634-638 ◽  
pp. 3569-3572 ◽  
Author(s):  
Yi Hua Dou ◽  
Xing Wang ◽  
Yang Yu ◽  
Xiang Tong Yang
Keyword(s):  
Contact Pressure ◽  
Equivalent Stress ◽  
Element Model ◽  
Linear Elastic ◽  
Axial Tension ◽  
Inner Pressure ◽  
Tension Load ◽  
Sealing Ability ◽  
Maximum Equivalent Stress ◽  
Maximum Contact

In order to know the sealing ability under axial alternating tension load, a 88.9mm×6.45mm P110 premium tubing connection is established with multiple linear elastic plastic finite element model, stress and contact pressure on sealing surface and torque shoulder are analyzed under axial alternating tension load and 80 MPa inner pressure. The results show that tubing connection slide by the axial tension, while the maximum contact pressure on seal surface reduced. With the increasing of alternating cycle, the maximum equivalent stress on seal surface increased and the maximum contact pressure on seal surface decreased. And, under limited loads, contact pressure on torque shoulder is affected little caused by alternating load.

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]

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

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.

Lower Bound Limit Load Estimation Using a Linear Elastic Analysis

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
C. Hari Manoj Simha ◽  
R. Adibi-Asl
Keyword(s):  
Lower Bound ◽  
Deformation Theory ◽  
Elastic Stress ◽  
Limit Load ◽  
Load Estimation ◽  
Elastic Analysis ◽  
Numerical Examples ◽  
Linear Elastic ◽  
Plastic Localization ◽  
Appl Math

We present a scheme that utilizes one elastic stress field (no iterations) to compute lower bound limit load multipliers of structures that collapse through gross (or localized) plasticity. A criterion to distinguish between these collapse modes is presented. For structures that collapse through gross plasticity, we demonstrate that the m′ multiplier proposed by Mura et al. (1965, Extended Theorems of Limit Analysis,” Q. Appl. Math., 23(2), pp. 171–179) is a lower bound in the context of deformation theory. For structures that undergo plastic localization at collapse, we present a criterion that identifies (approximately) the subvolumes of the structure that participate in the collapse. Multiplier m′ is computed over the selected subvolumes, denoted as m'S, and demonstrated to be a lower bound multiplier in the context of deformation theory. We consider numerical examples of structures that collapse by localized or gross plasticity and show that our proposed multiplier is lower than the corresponding multiplier obtained through elastic–plastic analysis and the proposed multiplier is not overly conservative.

scholarly journals Finite Element Modeling of Residual Stress at Joint Interface of Titanium Alloy and 17-4PH Stainless Steel

Metals ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 629
Author(s):  
Nana Kwabena Adomako ◽  
Sung Hoon Kim ◽  
Ji Hong Yoon ◽  
Se-Hwan Lee ◽  
Jeoung Han Kim
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Stainless Steel ◽  
Finite Element Modeling ◽  
Equivalent Stress ◽  
Stress Gradient ◽  
Joint Interface ◽  
Element Modeling ◽  
Actual Experiment ◽  
Maximum Equivalent Stress

Residual stress is a crucial element in determining the integrity of parts and lifetime of additively manufactured structures. In stainless steel and Ti-6Al-4V fabricated joints, residual stress causes cracking and delamination of the brittle intermetallic joint interface. Knowledge of the degree of residual stress at the joint interface is, therefore, important; however, the available information is limited owing to the joint’s brittle nature and its high failure susceptibility. In this study, the residual stress distribution during the deposition of 17-4PH stainless steel on Ti-6Al-4V alloy was predicted using Simufact additive software based on the finite element modeling technique. A sharp stress gradient was revealed at the joint interface, with compressive stress on the Ti-6Al-4V side and tensile stress on the 17-4PH side. This distribution is attributed to the large difference in the coefficients of thermal expansion of the two metals. The 17-4PH side exhibited maximum equivalent stress of 500 MPa, which was twice that of the Ti-6Al-4V side (240 MPa). This showed good correlation with the thermal residual stress calculations of the alloys. The thermal history predicted via simulation at the joint interface was within the temperature range of 368–477 °C and was highly congruent with that obtained in the actual experiment, approximately 300–450 °C. In the actual experiment, joint delamination occurred, ascribable to the residual stress accumulation and multiple additive manufacturing (AM) thermal cycles on the brittle FeTi and Fe2Ti intermetallic joint interface. The build deflected to the side at an angle of 0.708° after the simulation. This study could serve as a valid reference for engineers to understand the residual stress development in 17-4PH and Ti-6Al-4V joints fabricated with AM.

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