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.

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.

Finite Element Analysis in Orthopaedics

1987 ◽  
Vol 110 ◽  
Author(s):  
James B. Koeneman
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Beam Theory ◽  
Stress Distributions ◽  
Finite Element Analyses ◽  
Element Analysis ◽  
Bone Changes ◽  
Joint Implants ◽  
Bone Structures

AbstractPredicting the stress state in bones is important to the understanding of bone remodeling and the long-term reliability of total joint implants. Beam theory, 2-D and 3-D finite element analysis have been used to calculate stress distributions. These finite element analyses of bone structures are progressing from crude models for which the clinical relevance has been questioned to an important tool which is necessary to understand stress related bone changes.

Stress Predictions at Elbow Ends Under Internal Pressure and System Moments

2010 ◽  
Author(s):  
Jinhua Shi ◽  
Granson Lee ◽  
David Blythe ◽  
John Buckland ◽  
Yuebao Lei ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Internal Pressure ◽  
Hoop Stress ◽  
Stress Distributions ◽  
Finite Element Analyses ◽  
Central Section ◽  
Element Analysis ◽  
3D Finite Element ◽  
Hoop Stresses

In order to assess postulated defects in the butt weld joining a 90 degree elbow to a seamless straight pipe, both axial and hoop stress components at this position are required. ASME III NB-3685 provides a method of calculating elbow stresses. However, this gives the maximum stress values in the elbow and applies to the central section of the bend. If these values are directly used in the defect assessments of welds at the ends of the elbow, the assessment results will be overly conservative. In order to obtain appropriate defect assessment results, more accurate axial and hoop stress distributions at the elbow ends are desirable. In this paper, the axial and hoop stress distributions at the elbow ends are predicted by deriving generalized stress relationships between the elbow end and the central section of the elbow, based on detailed finite element analyses and ASME III NB-3685 calculations. In order to do so, a series of small displacement elastic 3D finite element analyses have been performed. The finite element results were then compared with the ASME III NB-3685 stress predictions. Finally, the axial and hoop stress relationships between the elbow end and the central section of the elbow for internal pressure, in-plane moment and out-of-plane moment were derived. A comparison of the calculated stress values using the derived equations, the finite element analysis results and the ASME III NB-3685 stress calculations confirms that the derived stress relationships are appropriate to predict the axial and hoop stresses at the elbow ends. The objective of this paper is to show: 1) the ASME III NB-3685 stress calculations agree well with the 3D finite element analysis results at the central section of the elbow and 2) the derived stress relationships are appropriate to predict the axial and hoop stresses at the elbow ends.

scholarly journals Comparison of Tooth- and Bone-Borne Appliances on the Stress Distributions and Displacement Patterns in the Facial Skeleton in Surgically Assisted Rapid Maxillary Expansion—A Finite Element Analysis (FEA) Study

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1152
Author(s):  
Rafał Nowak ◽  
Anna Olejnik ◽  
Hanna Gerber ◽  
Roman Frątczak ◽  
Ewa Zawiślak
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Element Model ◽  
Rapid Maxillary Expansion ◽  
Stress Distributions ◽  
Maxillary Expansion ◽  
Facial Skeleton ◽  
Element Analysis ◽  
Maxillary Constriction

The aim of this study was to compare the reduced stresses according to Huber’s hypothesis and the displacement pattern in the region of the facial skeleton using a tooth- or bone-borne appliance in surgically assisted rapid maxillary expansion (SARME). In the current literature, the lack of updated reports about biomechanical effects in bone-borne appliances used in SARME is noticeable. Finite element analysis (FEA) was used for this study. Six facial skeleton models were created, five with various variants of osteotomy and one without osteotomy. Two different appliances for maxillary expansion were used for each model. The three-dimensional (3D) model of the facial skeleton was created on the basis of spiral computed tomography (CT) scans of a 32-year-old patient with maxillary constriction. The finite element model was built using ANSYS 15.0 software, in which the computations were carried out. Stress distributions and displacement values along the 3D axes were found for each osteotomy variant with the expansion of the tooth- and the bone-borne devices at a level of 0.5 mm. The investigation showed that in the case of a full osteotomy of the maxilla, as described by Bell and Epker in 1976, the method of fixing the appliance for maxillary expansion had no impact on the distribution of the reduced stresses according to Huber’s hypothesis in the facial skeleton. In the case of the bone-borne appliance, the load on the teeth, which may lead to periodontal and orthodontic complications, was eliminated. In the case of a full osteotomy of the maxilla, displacements in the buccolingual direction for all the variables of the bone-borne appliance were slightly bigger than for the tooth-borne appliance.

scholarly journals 3D Finite Element Analysis of Rotary Instruments in Root Canal Dentine with Different Elastic Moduli

2021 ◽  
Vol 11 (6) ◽  
pp. 2547 ◽  
Author(s):  
Carlo Prati ◽  
João Paulo Mendes Tribst ◽  
Amanda Maria de Oliveira Dal Piva ◽  
Alexandre Luiz Souto Borges ◽  
Maurizio Ventre ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Root Canal ◽  
Elastic Moduli ◽  
Reaction Force ◽  
Von Mises Stress ◽  
Elastic Behavior ◽  
Element Analysis ◽  
Heat Treated ◽  
Von Mises

The aim of the present investigation was to calculate the stress distribution generated in the root dentine canal during mechanical rotation of five different NiTi endodontic instruments by means of a finite element analysis (FEA). Two conventional alloy NiTi instruments F360 25/04 and F6 Skytaper 25/06, in comparison to three heat treated alloys NiTI Hyflex CM 25/04, Protaper Next 25/06 and One Curve 25/06 were considered and analyzed. The instruments’ flexibility (reaction force) and geometrical features (cross section, conicity) were previously investigated. For each instrument, dentine root canals with two different elastic moduli(18 and 42 GPa) were simulated with defined apical ratios. Ten different CAD instrument models were created and their mechanical behaviors were analyzed by a 3D-FEA. Static structural analyses were performed with a non-failure condition, since a linear elastic behavior was assumed for all components. All the instruments generated a stress area concentration in correspondence to the root canal curvature at approx. 7 mm from the apex. The maximum values were found when instruments were analyzed in the highest elastic modulus dentine canal. Strain and von Mises stress patterns showed a higher concentration in the first part of curved radius of all the instruments. Conventional Ni-Ti endodontic instruments demonstrated higher stress magnitudes, regardless of the conicity of 4% and 6%, and they showed the highest von Mises stress values in sound, as well as in mineralized dentine canals. Heat-treated endodontic instruments with higher flexibility values showed a reduced stress concentration map. Hyflex CM 25/04 displayed the lowest von Mises stress values of, respectively, 35.73 and 44.30 GPa for sound and mineralized dentine. The mechanical behavior of all rotary endodontic instruments was influenced by the different elastic moduli and by the dentine canal rigidity.

Natural frequency analysis of a functionally graded rotor-bearing system with a slant crack subjected to thermal gradients

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arnab Bose ◽  
Prabhakar Sathujoda ◽  
Giacomo Canale
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Power Law ◽  
Beam Theory ◽  
Functionally Graded ◽  
Thermal Gradients ◽  
Element Analysis ◽  
Rotor Bearing ◽  
Natural Frequency Analysis ◽  
Bearing System

Abstract The present work aims to analyze the natural and whirl frequencies of a slant-cracked functionally graded rotor-bearing system using finite element analysis for the flexural vibrations. The functionally graded shaft is modelled using two nodded beam elements formulated using the Timoshenko beam theory. The flexibility matrix of a slant-cracked functionally graded shaft element has been derived using fracture mechanics concepts, which is further used to develop the stiffness matrix of a cracked element. Material properties are temperature and position-dependent and graded in a radial direction following power-law gradation. A Python code has been developed to carry out the complete finite element analysis to determine the Eigenvalues and Eigenvectors of a slant-cracked rotor subjected to different thermal gradients. The analysis investigates and further reveals significant effect of the power-law index and thermal gradients on the local flexibility coefficients of slant-cracked element and whirl natural frequencies of the cracked functionally graded rotor system.

scholarly journals Simulating sauropod manus-only trackway formation using finite-element analysis

2010 ◽  
Vol 7 (1) ◽  
pp. 142-145 ◽  
Author(s):  
P. L. Falkingham ◽  
K. T. Bates ◽  
L. Margetts ◽  
P. L. Manning
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Surface Area ◽  
Fossil Record ◽  
Temporal Correlation ◽  
Finite Element Analyses ◽  
Centre Of Mass ◽  
Element Analysis ◽  
Mass Distributions ◽  
Track Formation

The occurrence of sauropod manus-only trackways in the fossil record is poorly understood, limiting their potential for understanding locomotor mechanics and behaviour. To elucidate possible causative mechanisms for these traces, finite-element analyses were conducted to model the indentation of substrate by the feet of Diplodocus and Brachiosaurus . Loading was accomplished by applying mass, centre of mass and foot surface area predictions to a range of substrates to model track formation. Experimental results show that when pressure differs between manus and pes, as determined by the distribution of weight and size of respective autopodia, there is a range of substrate shear strengths for which only the manus (or pes) produce enough pressure to deform the substrate, generating a track. If existing reconstructions of sauropod feet and mass distributions are correct, then different taxa will produce either manus- or pes-only trackways in specific substrates. As a result of this work, it is predicted that the occurrence of manus- or pes-only trackways may show geo-temporal correlation with the occurrence of body fossils of specific taxa.

Investigation on stress distribution and pressure capacity of two-layer split high-pressure die based on finite element analysis

2019 ◽  
Vol 233 (14) ◽  
pp. 5048-5055
Author(s):  
Z Yi ◽  
WZ Fu ◽  
MZ Li
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
High Pressure ◽  
Stress State ◽  
Von Mises Stress ◽  
Stress Distributions ◽  
Element Analysis ◽  
Round Cylinder ◽  
Von Mises ◽  
Supporting Ring

In order to obtain a higher pressure capacity for the high-pressure die with a larger sample cavity, two types of two-layer split dies with a round cylinder and a quadrate cylinder were designed based on the conventional belt-type die. Finite element analysis was performed to investigate the stress distributions and pressure capacities of the high-pressure dies using a derived Mohr–Coulomb criterion and the von Mises criterion for the cylinder and supporting rings, respectively. As predicted by the finite element analysis results, in the two-layer split dies with a round cylinder, the stress state of the cylinder can be only slightly improved; and the von Mises stress of the first layer supporting ring can be hardly decreased. However, in the two-layer split dies with a quadrate cylinder and sample cavity, the stress state of the cylinder can be remarkably improved. Simultaneously, the von Mises stress of the supporting rings, especially for the first-layer supporting ring, can be also effectively decreased. The pressure capacities of the two-layer split dies with a round cylinder and a quadrate cylinder are 16.5% and 63.9% higher with respect to the conventional belt-type die.

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