A Finite Element Based Procedure for Simulating the Transient Response and Failure of a Two-Dimensional Continuum With Nonlinear Material Characteristics

1973 ◽  
Vol 95 (1) ◽  
pp. 345-352 ◽  
Author(s):  
D. B. Wallace ◽  
A. Seireg
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Impulsive Loading ◽  
Nonlinear Material ◽  
Two Dimensional ◽  
Arbitrary Geometry ◽  
Failure Patterns ◽  
Nonlinear Properties ◽  
Hollow Cylinders ◽  
Failure Theories

This paper presents a finite element based procedure for the analysis and graphic display of the response and failure patterns of a two-dimensional continuum subjected to impulsive loading. Elastic, anelastic, plastic and other nonlinear material properties and failure theories can be incorporated in the analysis. The procedure is illustrated by examples of elastic and anelastic impact of solid and hollow cylinders. The developed technique gives a powerful tool for the evaluation of transient stresses, deformations, yield and fracture modes in two-dimensional continuum with arbitrary geometry and nonlinear properties.

Fracture Prediction for the Proximal Femur Using Finite Element Models: Part I—Linear Analysis

1991 ◽  
Vol 113 (4) ◽  
pp. 353-360 ◽  
Author(s):  
J. C. Lotz ◽  
E. J. Cheal ◽  
W. C. Hayes
Keyword(s):  
Finite Element ◽  
Fracture Risk ◽  
Strain Gage ◽  
Proximal Femur ◽  
Material Properties ◽  
The United States ◽  
Nonlinear Material ◽  
Finite Element Models ◽  
Model Predictions

Over 90 percent of the more than 250,000 hip fractures that occur annually in the United States are the result of falls from standing height. Despite this, the stresses associated with femoral fracture from a fall have not been investigated previously. Our objectives were to use three-dimensional finite element models of the proximal femur (with geometries and material properties based directly on quantitative computed tomography) to compare predicted stress distributions for one-legged stance and for a fall to the lateral greater trochanter. We also wished to test the correspondence between model predictions and in vitro strain gage data and failure loads for cadaveric femora subjected to these loading conditions. An additional goal was to use the model predictions to compare the sensitivity of several imaging sites in the proximal femur which are used for the in vivo prediction of hip fracture risk. In this first of two parts, linear finite element models of two unpaired human cadaveric femora were generated. In Part II, the models were extended to include nonlinear material properties for the cortical and trabecular bone. While there was poor correspondence between strain gage data and model predictions, there was excellent agreement between the in vitro failure data and the linear model, especially using a von Mises effective strain failure criterion. Both the onset of structural yielding (within 22 and 4 percent) and the load at fracture (within 8 and 5 percent) were predicted accurately for the two femora tested. For the simulation of one-legged stance, the peak stresses occurred in the primary compressive trabeculae of the subcapital region. However, for a simulated fall, the peak stresses were in the intertrochanteric region. The Ward’s triangle (basicervical) site commonly used for the clinical assessment of osteoporosis was not heavily loaded in either situation. These findings suggest that the intertrochanteric region may be the most sensitive site for the assessment of fracture risk due to a fall and the subcapital region for fracture risk due to repetitive activities such as walking.

Probabilistic Models to Approximate Highly Repetitive Linear and Nonlinear Finite Element Analyses of Nuclear Components

2009 ◽  
Author(s):  
Dan Vlaicu ◽  
Mike Stojakovic
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Probabilistic Models ◽  
Nonlinear Material ◽  
Superposition Method ◽  
Loading Conditions ◽  
Finite Element Analyses ◽  
Axisymmetric Nozzle ◽  
Nonlinear Superposition ◽  
Pipe Bend

In the development and technical support of nuclear plants, Engineers have to deal with highly repetitive finite element analyses that involve modeling of local variations of the initial design, local flaws due to corrosion-erosion effects, material properties degradation, and modifications of the loading conditions. This paper presents the development of generic models that emulate the behavior of a complex finite element model in a simplified form, with the statistical representation based on a sampling of base-model data for a variety of test cases. An improved Latin Hypercube algorithm is employed to generate the sampling points based on the number and the range of the variables that are considered in the design space. Four filling methods of the approximation models are discussed in this study: response surface, nonlinear, neural networks, and piecewise polynomial model. Furthermore, a bootstrapping procedure is employed to improve the confidence intervals of the original coefficients, and the single-factor or double-factor analysis of variance is applied to determine whether a significant influence exists between the investigated factors. Two numerical examples highlight the accuracy and efficiency of the methods. The first example is the linear elastic analysis of a pipe bend under pressure loading. The objective of the probabilistic assessment is to determine the relation between the loading conditions as well as the geometrical aspects of this elbow (pipe wall thickness, outside diameter, elbow radius, and maximum ovality tolerance) and the maximum stress in the elbow. The second example is an axisymmetric nozzle under primary and secondary cycling loads. Variations of the geometrical dimensions, nonlinear material properties, and cycling loading are taken as the input parameters, whereas the response variable is defined in terms of Melan’s theorem translated into the Nonlinear Superposition Method.

Two Dimensional Plane Strain Modeling of Tube Hydroforming

2000 ◽  
Author(s):  
G. T. Kridli ◽  
L. Bao ◽  
P. K. Mallick
Keyword(s):  
Finite Element ◽  
Plane Strain ◽  
Material Properties ◽  
Thickness Distribution ◽  
Tube Hydroforming ◽  
Strain Hardening Exponent ◽  
Hydraulic Pressure ◽  
Two Dimensional ◽  
Dimensional Plane ◽  
Hydroforming Process

Abstract The tube hydroforming process has been used in industry for several years to produce components such as exhaust manifolds. Recent advances in forming machines and machine control systems have allowed for the introduction and the implementation of the process to produce several automotive components, which were originally produced by the stamping process. Components such as side rails, engine cradles, space frames, and several others can be economically produced by tube hydroforming. The process involves forming a straight or a pre-bent tube into a die cavity using internal hydraulic pressure, which may be coupled with controlled axial feeding of the tube. One of the remaining challenges facing product and process engineers in designing hydroformed parts is the lack of an extensive knowledge base of the process. This includes a full understanding of the process mechanics and the effects of the material properties on the quality of the hydroformed product. This paper reports on the results of two dimensional plane strain finite element models of the tube hydroforming process, which were conducted using the commercial finite element code ABAQUS/Standard. The objective of the study is to examine the effects of material properties, die geometry, and frictional characteristics on the selection of the hydroforming process parameters. The paper discusses the effects of the strain-hardening exponent, friction coefficient at the die-workpiece interface, initial tube wall thickness, and die corner radii on the thickness distribution of the hydroformed tube.

Nonlinear Transient Thermal Stress Analysis of Temperature-Dependent Hollow Cylinders Using a Finite Element Model

2014 ◽  
Vol 14 (07) ◽  
pp. 1450025 ◽  
Author(s):  
Ashraf M. Zenkour ◽  
Ibrahim A. Abbas
Keyword(s):  
Finite Element ◽  
Thermal Stress ◽  
Stress Analysis ◽  
Material Properties ◽  
Temperature Dependency ◽  
Temperature Dependent ◽  
Thermal Stress Analysis ◽  
Nonlinear Transient ◽  
Hollow Cylinders ◽  
Transient Thermal

In this paper, the nonlinear transient thermal stress analysis is conducted for temperature-dependent hollow cylinders subjected to a decaying-with-time thermal field. By the finite element method, the highly nonlinear governing equations are solved. The time histories of temperature, displacement, and stress due to the decaying-with-time thermal load are computed. A sensitivity analysis includes the effects of exponent of the decayed heat flux and temperature-dependency of density and material properties is carried out. Numerical results show some interesting characteristics of the thermoelastic behaviors of the hollow cylinders studied. In particular, the effect of temperature-dependency of the material properties on the thermoelastic parameters was demonstrated to be significant.

VLFEM Analysis of a Two-Dimensional Cochlear Model

1985 ◽  
Vol 52 (4) ◽  
pp. 743-751 ◽  
Author(s):  
C. E. Miller
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Basilar Membrane ◽  
Rate Of Change ◽  
Hybrid Technique ◽  
Two Dimensional ◽  
Arbitrary Boundary ◽  
Reflected Waves ◽  
Full Characterization ◽  
Optimal Mesh

A hybrid technique named here the Very Large Finite Element Method (VLFEM) is developed to analyze a two-dimensional model of the cochlea of the inner ear. In this method, the domain is divided into elements of constant material properties and the exact solution to the model equations obtained in each element. This involves two forms of eigenexpansion, allowing a one-dimensional instead of two-dimensional discretization. The discretization is related to the rate of change of the wavenumber of traveling waves on the elastic partition, producing an optimal mesh spacing. A full characterization of the multiple complex wavenumbers is obtained. The results of this analysis for partition (basilar membrane) amplitude and phase exactly correspond to those from previous finite difference and finite element analyses, but less computing effort is required for the same accuracy of results. Reflected waves, abrupt changes in material properties, and arbitrary boundary conditions pose no difficulties for VLFEM analysis, an advantage over the WKB (or LG) technique used previously on this problem.

Shakedown Analysis of Axisymmetric Nozzles Under Primary and Secondary Cyclic Loads

2009 ◽  
Author(s):  
Dan Vlaicu
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Stress Field ◽  
Material Properties ◽  
Cyclic Load ◽  
Elastic Stress ◽  
Nonlinear Material ◽  
Cyclic Loads ◽  
Shakedown Analysis ◽  
Elastic Plastic

In this paper, the finite element method is used to develop the lower bound limit for the elastic shakedown analysis of axisymmetric nozzles under periodic loading conditions. The Nonlinear Superposition Method is employed to calculate the lower bound shakedown loads by quoting Melan’s theorem in a nonlinear finite element analysis. The calculation is divided into two separate iterations which are blended with a technique that matches the elastic-plastic part of the analysis with the linear part. In the first part of the calculation, the cyclic load is applied as a static load to generate an elastic stress field in the structure. The same cyclic load is subsequently combined with the constant fraction of the load in the second part of the calculation, and the total load is applied in an elastic-plastic analysis that exceeds the yield limit. For each solution increment, the residual stress is generated from the superposition of the elastic stress field scaled through the applied cyclic load and the shakedown stress field calculated from the nonlinear analysis. The results obtained from the lower bound method are compared with the full cyclic loading analyses based on nonlinear material properties, and this paper discusses the choice of the global shakedown in terms of the radial strain, and the local through thickness shakedown defined by the hoop strain. Furthermore, this paper presents the development of a generic model that emulates the behavior of the finite element model under cyclic loads in a simplified form, with the statistical representation based on a sampling of base-model data for a variety of test cases. The probabilistic method takes variations of the geometrical dimensions, nonlinear material properties, and pressure load as the input parameters, whereas the response variable is defined in terms of the lower bound of the shakedown loads.

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