Bounded Elastic Moduli Multiplier Technique for Limit Loads: Part 2 - Case Studies

2021 ◽  
Author(s):  
Sathya Prasad Mangalaramanan
Keyword(s):  
Lower Bound ◽  
Case Studies ◽  
Power Law ◽  
Elastic Moduli ◽  
New Method ◽  
Stress Distributions ◽  
Limit Loads ◽  
Elastic Plastic ◽  
Thick Cylinder ◽  
Better Than

Abstract An accompanying paper provides the theoretical underpinnings of a new method to determine statically admissible stress distributions in a structure, called Bounded elastic moduli multiplier technique (BEMMT). It has been shown that, for textbook cases such as thick cylinder, beam, etc., the proposed method offers statically admissible stress distributions better than the power law and closer to elastic-plastic solutions. This paper offers several examples to demonstrate the robustness of this method. Upper and lower bound limit loads are calculated using iterative elastic analyses using both power law and BEMMT. These results are compared with the ones obtained from elastic-plastic FEA. Consistently BEMMT has outperformed power law when it comes to estimating lower bound limit loads.

Bounded Elastic Moduli Multiplier Technique for Limit Loads: Part 1 - Theory

2022 ◽  
Author(s):  
Sathya Prasad Mangalaramanan
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Lower Bound ◽  
Power Law ◽  
Elastic Moduli ◽  
Stress Distributions ◽  
Finite Element Analyses ◽  
Element Analysis ◽  
Limit Loads ◽  
Reduced Modulus

Abstract Statically admissible stress distributions are necessary to evaluate lower bound limit loads. Over the last three decades, several methods have been postulated to obtain these distributions using iterative elastic finite element analyses. Some of the pioneering techniques are the reduced modulus, r-node, elastic compensation, and linear matching methods, to mention a few. A new method, called the Bounded Elastic Moduli Multiplier Technique (BEMMT), is proposed and the theoretical underpinnings thereof are explained in this paper. BEMMT demonstrates greater robustness, more generality, and better stress distributions, consistently leading to lower-bound limit loads that are closer to elastoplastic finite element analysis estimates. BEMMT also questions the validity of the prevailing power law based stationary stress distributions. An accompanying research offers several case studies to validate this claim.

Can Repeated Elastic Analyses Always Provide Exact Limit Loads?

2002 ◽  
Author(s):  
Prasad Mangalaramanan
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Shear Stress ◽  
Power Law ◽  
Elastic Moduli ◽  
Past Research ◽  
Stress Distributions ◽  
Element Analysis ◽  
Limit Loads ◽  
Beam Bending

Past research showed that obtaining statically admissible stress distributions based on elastic moduli modification methods exactly correspond to stress distributions due to stress-strain power law, for beam bending and cylinder under internal pressure. This paper investigates shear stress redistribution based on modified elastic moduli, theoretical and inelastic finite element analysis methods.

A Design of High-Accuracy Displacement Measurement Instrument from Principles of Optics

2012 ◽  
Vol 170-173 ◽  
pp. 2924-2928
Author(s):  
Sheng Biao Chen ◽  
Yun Zhi Tan
Keyword(s):  
Measurement Instrument ◽  
High Accuracy ◽  
Mechanical Tests ◽  
Total Reflection ◽  
Displacement Measurement ◽  
New Method ◽  
Water Volume ◽  
Water Drainage ◽  
Accuracy Of Measurement ◽  
Better Than

In order to measure the water drainage volume in soil mechanical tests accurately, it develop a new method which is based on principles of optics. And from both physical and mathematic aspects, it deduces the mathematic relationship between micro change in displacement and the increment projected on screen. The result shows that total reflection condition is better than refraction condition. What’s more, the screen could show the water volume micro variation clearly, so it can improve the accuracy of measurement.

scholarly journals Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian

2021 ◽  
Author(s):  
Jürgen Jost ◽  
Raffaella Mulas ◽  
Florentin Münch
Keyword(s):  
Lower Bound ◽  
Bipartite Graph ◽  
Spectral Gap ◽  
Complete Bipartite Graph ◽  
Graph Laplacian ◽  
New Method ◽  
Single Edge ◽  
Largest Eigenvalue ◽  
Complement Graph ◽  
The Largest Eigenvalue

AbstractWe offer a new method for proving that the maxima eigenvalue of the normalized graph Laplacian of a graph with n vertices is at least $$\frac{n+1}{n-1}$$ n + 1 n - 1 provided the graph is not complete and that equality is attained if and only if the complement graph is a single edge or a complete bipartite graph with both parts of size $$\frac{n-1}{2}$$ n - 1 2 . With the same method, we also prove a new lower bound to the largest eigenvalue in terms of the minimum vertex degree, provided this is at most $$\frac{n-1}{2}$$ n - 1 2 .

Influence of Tooth Errors and Truing Principles of Grinding Wheel Abrasion for Machining Arc Enveloping Worm

2013 ◽  
Vol 652-654 ◽  
pp. 2153-2158
Author(s):  
Wu Ji Jiang ◽  
Jing Wei
Keyword(s):  
Mathematical Model ◽  
Case Studies ◽  
High Precision ◽  
High Performance ◽  
New Method ◽  
Grinding Wheel ◽  
Grinding Process ◽  
The Mathematical Model

Controlling the tooth errors induced by the variation of diameter of grinding wheel is the key problem in the process of ZC1 worm grinding. In this paper, the influence of tooth errors by d1, m and z1 as the grinding wheel diameter changes are analyzed based on the mathematical model of the grinding process. A new mathematical model and truing principle for the grinding wheel of ZC1 worm is presented. The shape grinding wheel truing of ZC1 worm is carried out according to the model. The validity and feasibility of the mathematical model is proved by case studies. The mathematical model presented in this paper provides a new method for reducing the tooth errors of ZC1 worm and it can meet the high-performance and high-precision requirements of ZC1 worm grinding.

Measurement of the Interfacial Stresses in Rolling Using the Elastic Deformation of the Roll

1987 ◽  
Vol 109 (4) ◽  
pp. 362-369 ◽  
Author(s):  
D. J. Meierhofer ◽  
K. A. Stelson
Keyword(s):  
Elastic Deformation ◽  
Normal Pressure ◽  
New Method ◽  
Frictional Stress ◽  
Stress Distributions ◽  
Strain Gages ◽  
Experimental Rolling ◽  
Mechanical Isolation ◽  
Roll Gap ◽  
Future Work

A new method to measure the frictional stresses and normal pressure in the roll gap during cold rolling, and experimental verification of this new method, are presented. The method overcomes many of the shortcomings of pin-type sensors. The elastic deformation of the roll itself is measured with strain gages, and is used to calculate the stresses between the sheet and the roll. Since no modification of the roll is necessary, the deformation process is undisturbed by the measurement. Mechanical isolation of the sensor is unnecessary. The mathematical procedure used to calculate the normal pressure and frictional stresses from the measured strains explicitly acknowledges that these strains are the result of the entire distribution of pressures and shears in the roll gap. An experimental rolling mill was constructed to verify the proposed method. Lead was rolled, and the resulting pressure and frictional stress distributions in the roll gap were measured. Several features of these distributions are in agreement with measurements made by various investigators using other techniques, thereby confirming the usefulness of the new method. Future work is proposed to increase the accuracy with which the roll gap stresses may be measured.

MASS FUNCTION OF HALOS: A NEW ANALYTICAL APPROACH

2004 ◽  
Vol 13 (07) ◽  
pp. 1345-1349 ◽  
Author(s):  
JOSÉ A. S. LIMA ◽  
LUCIO MARASSI
Keyword(s):  
Power Law ◽  
Free Parameter ◽  
Analytical Approach ◽  
Mass Function ◽  
New Method ◽  
Power Law Distribution ◽  
The Press ◽  
The Universe ◽  
Special Case

A generalization of the Press–Schechter (PS) formalism yielding the mass function of bound structures in the Universe is given. The extended formula is based on a power law distribution which encompasses the Gaussian PS formula as a special case. The new method keeps the original analytical simplicity of the PS approach and also solves naturally its main difficult (the missing factor 2) for a given value of the free parameter.

A Study of Wall Ironing by the Finite Element Technique

1978 ◽  
Vol 100 (1) ◽  
pp. 31-36 ◽  
Author(s):  
E. I. Odell
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Cone Angle ◽  
Reduction Ratio ◽  
Operating Parameters ◽  
Finite Element Technique ◽  
Elastic Plastic ◽  
Maximum Reduction ◽  
Load Displacement ◽  
Element Technique

Wall ironing has been analyzed using an elastic-plastic finite element technique. The effects that the ironing ring semi-cone angle and friction have on the maximum reduction ratio are studied in detail. Stress contours are given for a typical set of operating parameters. Several ram load/displacement curves are provided and compared with upper and lower bound loads.

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