Two-dimensional Stress Analysis Research Articles

Stress analyses of four prefabricated posts

A two-dimensional photoelastic stress analysis method was applied to study the relative magnitude of stress and concentration induced by four commercially available posts for endodontically treated teeth. Three types of threaded posts; VLock, Radix Anchor, and Flexi-Post, and one nonthreaded prefabricated post, the Para-Post Plus post were tested. Stress was recorded at installation, at vertical and inclined load, and the threaded posts were compared with the nonthreaded post. At installation and on loading, stress was induced where posts were in contact with the model. Higher apical stresses were demonstrated for the Para-Post Plus post whereas the threaded posts concentrated stress where they engaged the model through threads or flanges.

Three-Dimensional Stress Analysis for Bonded Dissimilar Materials.

The stress distribution introduced in joined dissimilar plates under tension was calculated from two-dimensional (2-D : the plane stress and plane strain states) and three-dimensional (3-D) elastic stress analyses using the finite-element method. A silicon nitride plate joined to copper plate was used. In the interfacial region of the composite specimen, a high stress concentration was found to occur, distributed three-dimensionally. Particularly, at the center of the specimen, the stresses, σx, in the direction of the applied stress, calculated from the 2-D and 3-D stress analyses, distributed quite differently near the interface. However, at a further distance from the interface, they agreed more closely. The highest stress, σx, appeared at the corners of the silicon nitride plate adjacent to the interface. Near the interface in the cross section of the specimen, the stresses calculated from the 3-D stress analysis varied rapidly, in contradiction to the assumption made in the 2-D analysis.

A Two-Dimensional Stress Analysis of Butt Adhesive Joints Filled with Rigid Circular Fillers in an Adhesive Subjected to Tensile Loads

This paper deals with a two-dimensional stress analysis of a butt adhesive joint with rigid fillers in an adhesive subjected to a tensile load. Assuming that adherends are rigid and replacing an adhesive with a finite strip including rigid fillers, the analysis was done using the two-dimensional theory of elasticity in order to examine the joint strength. The effects of the location and size of rigid fillers on the stress distributions around the fillers and at the interfaces were shown by numerical calculations. For verification, photoelastic experiments were performed. The analytical result was in fairly good agreement with the experimental result. It was seen that based on the amount of shift of the location and the filler diameter, the joint strength was more improved than that of the joints without fillers.

A Two-Dimensional Stress Analysis of a Butt Adhesive Joint Filled with Rigid Circular Fillers in the Adhesive Subjected to a Cleavage Load.

This paper deals with a two-dimensional stress analysis of a butt adhesive joint with rigid fillers in the adhesive subjected to a cleavage load. Similar adherends were replaced with finite strips, and an adhesive was replaced with a finite strip including rigid fillers. The analysis was done using the two-dimensional theory of elasticity in order to evaluate the joint strength. The effects of the location and size of rigid fillers on the stress distributions around the fillers and at the inter face were shown by numerical calculations. An experiment concerning the strains of adhesive was performed. The analytical result was consistent with the experimental result. It was seen that with an increase of the shift of location and size of fillers, the joint strength increased more than that of the joint without a filler. The stress singularity at the edge of the interface was discussed.

Stresses in silicon substrates near isolation trenches

We describe a methodology for obtaining stresses near isolation trenches in silicon considering the entire trench forming process. A two-dimensional plane strain finite element stress analysis is performed for a trench with a thermal SiO2 sidewall and polysilicon ‘‘fill’’ which includes the cumulative stresses from the superposition of (i) residual stresses from the thermal oxidation step, (ii) the intrinsic stress from the polysilicon deposition, and (iii) stresses due to the coefficient of thermal expansion mismatch between SiO2 and silicon during the temperature cycles involved in the process. The thermal oxidation step is simulated using a two-dimensional nonlinear viscoelastic program novel [in Proceedings of the Second International Symposium on Process Physics and Modeling in Semiconductor Technology, edited by G. R. Srinivasan, J. D. Plummer, and S. T. Pantelides (Electrochemical Society, Pennington, NJ, 1991), p. 772], that produces the oxide shape and stress at the oxide-silicon interface which is converted into equivalent nodal forces on the finite element grid. We have also made a three-dimensional finite element analysis of the thermal mismatch stresses between a parallelopipedic oxide inclusion in silicon with anisotropic properties and have compared these results with the analytical results [J. Appl. Phys. 66, 2741 (1989); 67, 1092 (1990)] in which the oxide and silicon are assumed to have identical isotropic elastic properties.

Accuratte evaluation of the singular integrals over quadratic boundary elements in 2D stress analysis

This paper is concerned with the evaluation of singular integrals in the boundary element method for two-dimensional stress analysis. Analytical processes are applied to the singular integrals over curved quadratic boundary elements on the basis of coordinate trasnformations. The Cauchy-type integrals are reduced to the regular ones, the computation of which can be performed analytically as well as numerically by using standard Gaussian quadrature formulae. Examples show the numerical stability and efficiency of the present procedure. Finally a useful technique is proposed i.e., that the accurate values of the Cauchy-type integrals can be used to appraise the accuracy of the off-diagonal coefficients of matrix H with the help of the rigid-body motion technique.

Singular integral operators method for two-dimensional elasto-plastic stress analysis

The Singular Integral Operators Method is presented for the formulation of the two-dimensional elasto-plastic stress analysis. The formulation of the two-dimensional elasto-plastic problem is stated, by applying the fundamental solutions for an isotropic solid. The most interesting features of this method are the much smaller systems of equations and considerable reduction in the data required to run the elasto-plastic problem. An application is presented, to the determination of the stress field in the neighborhood of a circular hole under internal pressure in an infinite and isotropic solid. A second application is stated, to the determination of the plastic behaviour of a square block compressed by two opposite perfectly rough rigid punches in plane strain.

Finite element analysis of an elastic-plastic two-layer half-space: sliding contact

A two-dimensional finite element stress and strain analysis of the sliding contact of a two-layer elastic-plastic half-space for various friction coefficients was conducted. First the contact pressure of the two-layer half-space under normal indentation was determined. Then the normal and tangential loadings were applied proportionally and incrementally on the surface. It was found that surface deformation, location of initial yielding, stresses and strains along the interfaces between layers strongly depend on the friction coefficient. When the friction coefficient is small (less than 0.3), yielding initiates in the subsurface region near the leading edge of the contact, provided that the normal load is large enough. When the friction coefficient is large (greater than 0.3), yielding initiates on the surface at the trailing edge of the contact. The surface strains, especially the shear strains, are large owing to the unconstrained deformation. The magnitudes of shear stresses and strains along both interfaces are significantly large for high friction. On the basis of the analysis, the implications for interface failures are qualitatively addressed.

Thermomechanical behaviour of thin oxide coatings

For an optimal selection of structural materials in practical applications it is important to obtain detailed knowledge of the mechanical load on the system. Usually it is very difficult to judge these load conditions, especially in composites, for example ceramic layers on metallic substrates. Starting from experimental findings on the damage behaviour of a special oxide/metallic substrate system, an elementary analytical model is derived in the first part of this paper. This model describes the mechanical loadings of the layer and is additionally compared with a more detailed two-dimensional numerical stress analysis. The following experimental results, concerning the state of mechanical stress in the coatings, which were determined by mechanical testing as well as by X-ray stress evaluation, are in good agreement with theoretical predictions.

Boundary element analysis of elasto-plastic contact problems

In this paper a boundary element method for two-dimensional elasto-plastic stress analysis of frictional contact problems is presented. The bodies in contact are treated as separate regions. The contact conditions are used to join the different system of equations for different regions of contacted bodies and hence an overall system of equations would be obtained. An incremental and iterative procedure can be used to find the contact load, or the contact extent and the proper contact conditions. To include the plastic deformation in the analysis the initial strain algorithms is employed. Elastic-perfectly plastic or work-hardening material behavior can be assumed. For the numerical analysis, isoparametric three-noded line elements are used to represent the boundary and eight-noded quadrilateral and six-noded triangular elements are used for the interior of the domain. The displacement rates and traction rates are assumed to vary quadratically and the shape functions for the interior strain rates are also of quadratic type. As an example the behavior of an elastic and elasto-plastic body with a smooth, circular inclusion under the increasing load is presented.

A Two-dimensional Stress Analysis of Butt Adhesive Joints Having a Circular Hole Defect in the Adhesive Subjected to External Bending Moments

Abstract This paper deals with a two-dimensional stress analysis of butt adhesive joints, with a circular hole defect in the adhesive, subjected to external bending moments. The analysis was done using the two-dimensional theory of elasticity in order to examine the strength of the joints. It was assumed that the adherends were rigid and the adhesive was replaced with a finite strip including a hole defect. The effects of the location and size of a hole defect on the stress distributions around the hole and at the interfaces were obtained by numerical calculations. In addition, the singular stress near the edge of the interface was obtained. For verification, photoelastic experiments were performed. The analytical results were fairly consistent with the experimental results. It was seen that the principal stress around a hole becomes larger with a certain shift toward the free boundary. It was also seen that the stress concentration became larger with an increase of the size of the hole.

A Two-Dimensional Stress Analysis of Butt Adhesive Joints Filled With Rigid Circular Fillers in an Adhesive Subjected to External Bending Moments.

This paper deals with a two-dimensional stress analysis of butt adhesive joints with rigid fillers in an adhesive subjected to external bending moments. Assuming that adherends are rigid, and replacing an adhesive with a finite strip including rigid fillers, the analysis was performed using the two-dimensional theory of elasticity in order to examine the strength of joints. The effects of the location and size of rigid fillers on the stress distributions around the fillers and at the interface were shown by numerical calculations. For verification, photoelastic experiments were performed. The analytical result was in fairly good agreement with the experimental result. It was seen that due to the amount of shift of location and size of fillers, the strength of joint was more improved than that of the joints without a filler. The stress singularity at the edge of the interface was discussed.

Two-dimensional stress analysis of adhesive butt joints subjected to cleavage loads

This paper deals with the two-dimensional stress analysis of adhesive butt joints subjected to cleavage loads. The purpose of the paper is to contribute to the establishment of fracture criteria of adhesive joints. Similar adherends and an adhesive bond are replaced with finite strips in the analysis. Stress distributions in adhesive joints are analysed using the two-dimensional theory of elasticity. The effects of the ratio of Young's modulus of adherends to that of an adhesive and the thickness of the adhesive bonds on the stress distributions are shown by numerical calculations. For verification, strains produced on adherends are experimentally measured and a photoelastic experiment is carried out. The analytical results are in fairly good agreement with experiment.

Two-dimensional stress analysis of adhesive butt joints subjected to cleavage loads

Two-dimensional stress analysis of adhesive butt joints subjected to cleavage loads

TRANSIENT THERMAL STRESS AND DEFORMATION OF A LAMINATED COMPOSITE BEAM DUE TO PARTIALLY DISTRIBUTED HEAT SUPPLY

Abstract This paper is concerned with a two-dimensional transient thermal stress analysis of a laminated beam due to a partially distributed heat supply. The beam is composed of different materials in multilayers. For the laminated composite beam we use the finite cosine transform and the Laplace transform for the temperature field and we adapt the elementary beam theory to the thermoelastic field. We then evaluate the temperature change, thermal stress distribution, and thermal deformation in a transient state. We apply the proposed theoretical method to the analysis of a beam with nonhomogeneous material properties, and examine the distributions of thermal stress and thermal deformation and the effect of relaxation of the stress distributions in a nonhomogeneous beam.

Two-dimensional unsteady thermal stress analyses by means of the boundary element method.

The boundary element method (BEM) has been used in various fields because BEM is convenient compared to FEM. BEM does not need an area integral in two-dimensional elastic problems without body forces, but in unsteady two-dimensional thermoelastic problems, the area integral is usually necessary. A method of transforming the area integral in BEM for two-dimensional unsteady thermoelasticity to a boundary integral has been recently reported [1]. However, a cell was used in a numerical example, and the time integral was carried out numerically. This paper shows that the time integral can be carried out analytically. The values of the stress discontinuities on the boundary are also clarified. In conclusion, it is shown that the same equation can be used in both the internal area and on the boundary.

A basic study of the accuracy estimation of structural analysis by the zooming method. 4th Report, Two-dimensional elastostatic stress analysis by the boundary element method.

In boundary element analysis using the zooming method. the error of the stress at the selected point is expected to be smaller than the sum of two errors. One is the error caused by the mesh diameter of the original boundary. The other is the error of displacement on a zooming boundary. Using the self-adaptive mesh refinement technique, the former becomes smaller than the allowable error. The latter can be estimated by the relation between the mesh diameter and the error in the recursive analyses. A computer program using this error estimation method was developed and applied to several problems of various shapes. The usefulness of this accuracy estimation method was illustrated by these application results.

A two-dimensional stress analysis of butt adhesive joints filled with rigid circular fillers in an adhesive subjected to tensile loads.

This paper deals with a two-dimensional stress analysis of butt adhesive joints with rigid fillers in an adhesive subjected to tensile loads. Assuming that adherends are rigid and replacing an adhesive with a finite strip including rigid fillers, the analysis was done using the two-dimensional theory of elasticity in order to examine the strength of joints. The effects of the location and size of rigid fillers on the stress distributions around the fillers and at the interface were shown by numerical calculation. For verification, photoelastic experiments were performed. The analytical result was in fairly good agreement with the experimental result. It was seen that by an amount of shift of location and size of fillers, the strength of joints was more improved than that of the joints without a filler. Discussion is also presented on the stress singularity at the edge of the interface.

A two-dimensional stress analysis of band adhesive butt joints subjected to tensile loads. The case of finite strip adherends.

In this paper, the stresses of band adhesive butt joints, in which adhesive bonds were used partially at the interfaces, were analyzed using a two-dimensional theory of elasticity in order to determine the usefulness of the joints. In the analysis, similar adherends and adhesive bonds which were set at two or three regions were replaced with finite strips. In numerical computations, the effects of the ratio of Yound's modulus of adherends to that of adhesives, the thickness of the adhesives, the bonding area and position, and the load distribution on the stress distributions at the interface were shown. It was seen that band adhesive joints were effective when the bonding area and positions were varied with external load distributions. Photoelastic experiments and experiments concerning the strains of adherends were performed. The analytical results were fairly consistent with the experimental results.

A two-dimensional stress analysis of band adhesive butt joints subjected to external bending moments.

The stresses of band adhesive butt joints subjected to external bending moments, in which adhesive bonds were used partially at the interface, were analyzed using a two-dimensional theory of elasticity in order to establish the fracture criteria of joints. Similar adherends and adhesive bonds which were used at two or three regions at the interface were replaced with finite strips in the analysis. In numerical computations, the effects of the ratio of Young's modulus of adherends to that of adhesives, the thickness of the adhesive and the bonding area and positions on the stress distributions at the interface were shown. It was found that band adhesive joints were effective when the bonding area and positions were varied with external load distributions. The stress distribution near the singular point at the interface were expressed approximately. Photoelastic experiments and experiments concerning the strains of adherends were performed. The analytical results were fairly consistent with the experimental results.