Non-axisymmetric Loading Research Articles

AN AXISYMMETRIC JOINT ELEMENT UNDER NON-AXISYMMETRIC LOADINGS IN SEMI-ANALYTICAL FINITE ELEMENT METHOD

A new axisymmetric joint element model for semi-analytical finite element analysis of axisymmetric bodies subjected to non-axisymmetric loading is proposed. The new joint element model for axisymmetric interface has three degrees of freedom: normal tangential and circumferential directions and describes debonding (normal direction), and slip (tangential and circumferential direction) on the interface. The new joint element model was incorporated into a finite element program and test-case analyses were performed. The results indicate that the new joint element model is useful in the semi-analytical finite element analysis for deeper understanding of stress distributions on the axisymmetric interface.

Dynamic stability of cylindrical shells under nonaxisymmetric loading

Dynamic stability of cylindrical shells under nonaxisymmetric loading

Material Constants for a Finite Element Model of the Intervertebral Disk With a Fiber Composite Annulus

A simple axisymmetric finite element model of a human spine segment containing two adjacent vertebrae and the intervening intervertebral disk was constructed. The model incorporated four substructures: one to represent each of the vertebral bodies, the annulus fibrosus, and the nucleus pulposus. A semi-analytic technique was used to maintain the computational economies of a two-dimensional analysis when nonaxisymmetric loads were imposed on the model. The annulus material was represented as a layered fiber-reinforced composite. This paper describes the selection of material constants to represent the anisotropic layers of the annulus. It shows that a single set of material constants can be chosen so that model predictions of gross disk behavior under compression, torsion, shear, and moment loading are in reasonable agreement with the mean and range of experimentally measured disk behaviors. It also examines the effects of varying annular material properties.

Application of ring elements in the nonlinear analysis of shells of revolution under nonaxisymmetric loading

A problem-oriented method for the nonlinear elastic-plastic analysis of nonsymmetrically loaded shells of revolution is described. It is based on an approximation of the circumferential distribution of the loads and variables by Fourier series. Ring finite elements are used in the axial direction. Their stiffness matrices are obtained by accurate numerical integration rather than by trial functions. To be able to take full advantage of the Fourier decomposition and the one-dimensional discretization, all nonlinearities are treated iteratively in the form of pseudo-load vectors. Thus, the various Fourier harmonics are governed by uncoupled algebraic equations and no explicit knowledge of the nonlinear global tangent stiffness matrix is required. Convergence problems of the iterative procedure are avoided by employing a sort of conjugate gradient method with a special preconditioning within each increment. Numerical examples involving strongly nonlinear behavior and highly nonsymmetric states of stress and deformation are given which demonstrate the effectiveness of the method.

STRESS DISTRIBUTION ON THE CONNECTION BETWEEN PILE-HEAD AND FOOTING OF PILE FOUNDATION

In this paper, it is investigated that how axial load and buried length of pile-head into footing under lateral load effect on the stress distribution of footing concrete on pile-footing interface. For the evaluation of the effects, the connection between pile-head and footing is treated as an axisymmetric body subjected to non-axisymmetric loading. and the evaluation is performed by Finite Element Analysis. For the analysis, it is assumed that debonding or slip never occur on the interface.The results suggest that axial load and buried pile-head length have significant effects on the stress distribution, and the cohesion on the interface is very significant factor on the stress distribution.

Stability of the anisotropy of a cylindrical shell under a nonaxisymmetric load

Stability of the anisotropy of a cylindrical shell under a nonaxisymmetric load

Action of nonaxisymmetric normal load over the surface of an elastic shell interacting with a liquid

Action of nonaxisymmetric normal load over the surface of an elastic shell interacting with a liquid

Axisymmetric thermoelastic-plastic stress-strain state of branched shells with simple loading processes

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Prediction of Leakage Gap in Nonaxisymmetric Geometry Face Seals

With the recognition that seal faces are not perfectly flat and/or that nonaxisymmetric seal loading will cause seal faces to distort, there is a need to predict whether or not a leakage gap will result. If a gap does occur, it is then necessary to predict its size and circumferential variation. In this paper, a tool for predicting seal gap is developed. The method is general. Initial face profiles are arbitrary. Ring cross-sections and seal loading may vary circumferentially. The model uses the stiffness properties of a general ring finite element and couples the two rings by a series of springs which represent contact at the face. The entire problem is solved using a finite element method. The seal load is incremented so that as deflection increases, springs representing face contact are included in the problem as required. The final result is seal gap as a function of angular position or contact pressure at points where the faces touch. The model has been verified experimentally using two rings with an eccentric load which causes a gap to develop. Agreement with the experiment is good. The model is also used to predict leakage gap in some magnetically loaded commercial seals. A comparison between predicted leakage and measured leakage is made and the comparison is good. The model should find wide application in providing accurate analysis for seal leakage problems. It can be used to establish flatness guidelines as well as to show the effects of nonaxisymmetric loading on seal leakage.

Axisymmetric shells for non-axisymmetric loads: an exact conical element approach

A program to solve axisymmetric shell structures for non-axisymmetric loading is presented. The structure is divided into conical elements. Exact classical shell equations are used for each element. The displacements and external loads are then developed in Fourier series in the hoop direction, and the resulting diffential equations are solved by means of analytical functions of the potential series type. Circular beams connected at elements interface are also considered. A computer program that can be used for a wide variety of problems is then developed. It is applied, as an example, to a ball mill, used normally in the mining industry. The method showed an excellent behaviour in different examples. No more than 20 elements were needed in the potential series to get a relative error of less than 10 −3.

Mechanical response of a simple finite element model of the intervertebral disc under complex loading

A simple axisymmetric finite element model of a human spine segment containing two adjacent vertebrae and the intervening intervertebral disc was constructed. The bodies and disc were modeled by three substructures; one to represent each of the vertebral bodies, the annulus fibrosus, and the nucleus pulposus. A semi-analytic technique was used to maintain the computational economies of a two-dimensional analysis when non-axisymmetric loads were imposed on the model. The response of the model to compression, shear, torsion and bending loads applied to the superior vertebral body was examined to determine the effects of disc geometry and material properties on response. Comparisons of model responses with experimentally measured responses were made to estimate material property values for which model behaviors are in agreement with measured behaviors.

Analysis of nonsteady processes caused by nonaxisymmetric loading of multilaminate finite cylinders

UDC 539.4 Many actual processes connected with impulsive loads on structures fall into the class of axisymmetric problems. The methods of solving such problems are well developed, and there are many examples of successful numerical integration of one- and two-dimensional problems of continuum mechanics [1-3]. There are considerably fewer examples of the solution of three-dimensional dynamic problems. Together with this, problems of studying the dynamic behavior of non-thin-walled structures and of component structures containing zones of rapid change in geometry or the mechanical properties of the material, as well as problems of the propagation of very short waves in structural elements, cannot be solved without consideration of the three-dimensionality of the stress-strain state. The present work briefly describes an algorithm for calculating the three-dimensional stress-state of multilaminate finite cylinders subjected to nonaxisymmetric loading. The layers of the cylinders are made of different materials. The layers are rigidly fastened to each other without a negative allowance. The external surface is acted upon by a pressure pulse of duration 10-5-10 -9 sec. This pulse arrives at the cylinder surface at t = 0 and is distributed according to a cosine law in the peripheral direction. The effectiveness of the algorithm will be demonstrated using the example of calculation of waves generated in two-layer cylinders under the action of a very brief load. It should be noted that the strength of structures subjected to intensive short-time loading is determined by processes of different duration. The first process involves the formation and propagation of compression waves in the body. These waves may lead to fracture of the body when they reach its surface. The likelihood of fracture depends on the spall strength of the material of the body and the location of the fastenings or joints between the structural elements. In the second process, strength is determined less and less by wave processes, and it begins to depend on the dynamics of deformation of the body as a whole. Below, we limit our calculations to an examination of the initial wave processes in a multilaminate body.

Sensitivity of Estimated Tube Life to Material Property Variation

The estimated tube life of the Incoloy 800 tubes of a solar receiver panel under nonaxisymmetric loading is compared for various material property assumptions. The basis of each life evaluation is an elastic-creep analytical study of up to 20 load cycles. The effect on tube life of a variation in the creep rate for the failure modes of creep ratcheting and creep fatigue is studied in some detail. As shown for these elastic-creep conditions, the creep damage and mean diametral strain accumulations per cycle decrease linearly over the calculated 20 cycles when plotted against cycle number on a log-log scale. The predictions of total creep damage and mean diametral strain in 10,000 cycles based on the extrapolated log-log scale curve are substantially lower than the predictions based on multiplication of the change in value of the 20th day of operation by 10,000. A limited evaluation of the effects of variations in other material parameters is also made.

An analysis of tibial component design in total knee arthroplasty

An axisymmetric finite element model of the proximal tibia and cemented tibial component subject to nonaxisymmetric loading is presented. Model variations included polyethylene components and steel reinforced polyethylene components both with and without a central fixation post. Central fixation posts of 35 and 70 mm were modeled. A vertically oriented lead applied unilaterally to the tibial component was found to generally cause the largest magnitude peak stresses within the various components of the structure. The addition of steel reinforcement to tibial components without central fixation post is predicted to significantly reduce stress levels within the polymethylmethacrylate and underlying cancellous bone. Although to a lesser extent, the addition of a relatively short central fixation post to the steel reinforced tibial component further reduced these stress levels. The longer steel central fixation post can appreciably reduce proximal cement and bone stress levels. The tibial component condylar width is predicted to have little effect on polymethylmethacrylate and cancellous bone stresses, with the exception that proximal tibial cancellous bone compressive stresses are reduced with wide steel reinforced components.

Design for Minimum Stress Concentration by Finite Elements and Linear Programming

ABSTRACT The problem of design for minimum stress concentration is highly nonlinear and must be solved iteratively. Each iteration (redesign) involves three steps: an analysis of the stresses for a design, a sensitivity analysis corresponding to possible changes in this design, and the decision of redesign. For stress analysis, the FEM is a unified approach which is applied in the present paper to axisymmetric solids that are also subjected to nonaxisymmetric loads. The decision of redesign is a linear programming problem and can thus be solved with the Simplex algorithm. The introduction of move-limits to the formulation is of major importance. The optimization approach is described in general, but most of the paper concentrates on a specific example and shows optimum shapes of a shoulder fillet in a stepped bar. Loads are bending, tension, or torsion, and the stress concentrations are considerably reduced.

An axisymmetric model of acetabular components in total hip arthroplasty

An axisymmetric finite element model with nonaxisymmetric loading of an acetabular arthroplasty and the surrounding pelvic bone is presented. Model variations include ultra high density polyethylene acetabular components of varying wall thicknesses and metal backed ultra high density polyethylene components. Each of the two component types is modeled as implanted within an acetabulum with intact subchondral bone and within an acetabulum without subchondral bone. Thin wall polyethylene acetabular prostheses are predicted to increase, relative to thick wall components, maximum stresses in the cement-bone composite. Trabecular bone stresses are predicted to increase with the removal of subchondral bone. Stiffer metal-backed acetabular components are predicted to reduce maximum cement and bone stresses and to abridge the effects of altered component wall thickness and of subchondral bone removal.

Thermoelastoplastic stress state of an open shell of revolution under nonaxisymmetric mechanical and thermal loads

Thermoelastoplastic stress state of an open shell of revolution under nonaxisymmetric mechanical and thermal loads

A semi-analytic finite-element analysis of circular plate bending problems

Semi-analytic formulations have previously been used for a number of stressing problems wherein axisymmetric structures have supported non-axisymmetric loads. The approach is here shown to be very useful for circular plates, and to have especial value for design analyses using desk top computers in which the main store is relatively small.

IPAC — an interface software system for model development

IPAC is an interface software system which allows a user to access other finite element program through minimum input instructions. The system is built around GIFTS 5—a modular and interactive graphics oriented finite element program. The dual system provides many user-oriented features and much flexibility of use to meet a wide variety of applications. Variable node 3-D isoparametric element generation capability has been introduced for bodies of revolution. Wheels, torus, rings or similar bodies of irregular cross-sections can now be easily modelled using this feature and can be analysed under nonaxisymmetric loadings. The system allows selected input and calculated data to be extracted, manipulated and displayed via on-line or off-line prints or plots for monitoring and verifying model generations. IPAC is intended for use in a production environment where the case studies are to be done on the geometry requiring creation of several finite element models with variations in elements, grid size or boundary conditions. The system is organized to be machine independent and modular to facilitate its maintenance and to render new developments quickly and easily.

Coupled Vibrations of a Structure and Fluid Excited by Pressure Shocks

The dynamic behavior of an axisymmetric boiling water reactor suppression pool structure and the embedded water under the excitation of the pressure waves from collapsing steam bubbles was studied with a finite element model. The structure was analyzed with thin shell elements. The fluid volume is divided into isoparametric quadrilateral toroidal elements with pressure as the nodal parameter. A water source element was utilized to model the pressure shock excitation. Nonaxisymmetric pressure loads and vibration modes were expressed as a Fourier series in the circumferential coordinate. The system of equations for the structure and fluid was integrated in time using the central difference scheme.