Two-dimensional Stress Analysis Research Articles

Two-Dimensional Unsteady Thermal Stress Analysis by Triple-Reciprocity BEM.

If initial temperature is assumed to be constant, a domain integral is not required for solution of unsteady thermal stress problems without heat generation using the boundary element method (BEM). However, under heat generation or nonuniform initial temperature distribution, the domain integral is necessary. In this report it is shown that the problem of unsteady heat conduction with heat generation and nonuniform initial temperature can approximately be solved without use of the domain integral by a triple-reciprocity boundary element method. In this method, the distribution of heat generation and initial temtepature are interpolated by using integral equation.

The Effective Friction Coefficient of a Laminate Composite, and Analysis of Pin-Loaded Plates

A calculation method based on M-CLT (Modified Classical Lamination Theory) for the friction coefficient of a CFRP (Carbon Fiber Reinforced Plastic) composite laminate edge is proposed. It is derived based on experimental friction coefficients in unidirectional off-axis laminae and a high-order algebraic equation from a numerical solution to the specific boundary for the frictional contact problem. A numerical experiment of a frictional contact problem is also performed by means of a nonlinear three-dimensional finite element analysis and the results are compared with those obtained from the M-CLT method for various contact directions. Good agreement is found between the two sets of results. Finally, the friction coefficient derived by using the M-CLT method is applied to a two-dimensional contact stress analysis of a pin-loaded composite laminate. The effects of the method used to calculate the friction coefficient on the contact stress distribution are investigated.

The Effective Friction Coefficient of a Laminate Composite, and Analysis of Pin-loaded Plates

A calculation method based on M-CLT (Modified Classical Lamination Theory) for the friction coefficient of a CFRP (Carbon Fiber Reinforced Plastic) composite laminate edge is proposed. It is derived based on experimental friction coefficients in unidirectional off-axis laminae and a high-order algebraic equation from a numerical solution to the specific boundary for the frictional contact problem. A numerical experiment of a frictional contact problem is also performed by means of a nonlinear three-dimensional finite element analysis and the results are compared with those obtained from the M-CLT method for various contact directions. Good agreement is found between the two sets of results. Finally, the friction coefficient derived by using the M-CLT method is applied to a two-dimensional contact stress analysis of a pin-loaded composite laminate. The effects of the method used to calculate the friction coefficient on the contact stress distribution are investigated.

Stress Transfer in the Fiber/Matrix Interface of Titanium Matrix Composites Due to Thermal Mismatch and Reaction Layer Development

It is well known that the difference in the coefficient of thermal expansion of the components of titanium matrix composites with the SCS-6 SiC-fiber gives rise to substantial residual stresses. Due to the fact that the fiber/matrix bond strength is low (as long as there is still a substantial thick carbon protection layer) fiber/matrix stress transfer is realized partly through interfacial friction enabled by the residual radial compressive stress at the fiber/matrix interface. Fiber matrix reactions usually lead to a volume change. In the present investigation this volume change is investigated analytically as well as experimentally on the SCS-6/IMI834 system. It was determined analytically with the aid of a two-dimensional stress analysis that fiber/matrix reaction leads to a reduction of the residual stresses. Experimental results on composite specimen diameter change indicate an increase of the residual stress caused by an unexpected shrinkage of the matrix. Another source for residual stress is an unequal (inwards and outwards) radial growth of the reaction layer if the diffusion rate of the reacting species through the reaction layer differs from the stoichiometric relation for the reaction.

A two-dimensional stress analysis of single-lap adhesive joints of dissimilar adherends subjected to tensile loads

Single-lap adhesive joints of dissimilar adherends subjected to tensile loads are analyzed as a three-body contact problem using the two-dimensional theory of elasticity. In the numerical calculations, the effects of Young's modulus ratio between different adherends, the ratio of the adherend thicknesses, the ratio of the adherend lengths, and the adhesive thickness on the contact stress distributions at the interfaces are examined. As a result, it is found that (1) the stress singularity occurs near the edges of the interfaces and it increases at the edge of the interface of an adherend with smaller Young's modulus; (2) the stress singularity increases at the edge of the interface of an adherend with thinner thickness; (3) the singular stresses increase at the edges of the two interfaces as the ratio of the upper adherend length to the lower one decreases; and (4) the singular stresses increase at the edges of the two interfaces as the adhesive thickness decreases when the adhesive is thin enough, and they also increase as the adhesive thickness increases when the adhesive is thick enough. In addition, the singular stresses obtained from the present analysis are compared with those obtained by Bogy. Fairly good agreement is seen between the present analysis and the results from Bogy. Strain measurement and finite element analysis (FEA) were carried out. The analytical results are in fairly good agreement with the measured and the FEA results.

A coding error elimination procedure for verifying finite element programs with forced and natural boundary conditions

The general procedure developed by Shih for eliminating computer coding errors has been both simplified for finite element applications and extended for use in the verification of the coding of forced and natural boundary conditions. To accomplish these two objectives simultaneously, use is made of volume weighted residuals for all elements within the solution regime and of area weighted boundary residuals for all elements having natural boundary conditions on one or more of their borders. This procedure can thus be used to verify finite element codes with a combination of both forced (Dirichlet) and natural (Neumann and Robbins) boundary conditions. Depending on the equations being solved and the boundary conditions they are being subjected to, this modification can make possible the implementation of Shih's general procedure into existing finite element codes without having to carry out any additional discretization steps. The employment of this modified procedure is illustrated using two-dimensional (2-D) stress analysis and transient heat conduction problems. Copyright © 1999 John Wiley & Sons, Ltd.

A Two-dimensional Stress Analysis and Strength of Single-lap Adhesive Joints of Dissimilar Adherends Subjected to External Bending Moments

The stress distributions of single-lap adhesive joints of dissimilar adherends subjected to external bending moments are analyzed as a three-body contact problem by using a two-dimensional theory of elasticity (plane strain). In the analysis, dissimilar adherends and an adhesive are replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli of adherends, the adherend thickness ratio and the adherend length ratio between dissimilar adherends on the stress distributions at the interfaces are examined. The results show that the stress singularity occurs at the ends of the interfaces, and its intensity is greater at the interface of the adherend with smaller Young's modulus. It is also noted that the singular stress is greater at the interface of the thinner adherend. It is found that the effect of the adherend length ratio on the stress singularity at the interfaces is very small. Joint strength is predicted by using the interface stress and it was measured by experiments. From the analysis and the experiments, it is found that the joint strength increases as Young's modulus of adherends and the adherend thickness increase while the effect of the adherend lengths on the joint strength is small. For verification of the analysis, a finite element analysis (FEA) is carried out. A fairly good agreement of the interface stress distribution is seen between the analytical and the FEA results.

A two-dimensional finite element thermal stress analysis of adhesive butt j oints containing some hole defects

Thermal stress distributions in adhesive butt joints containing some hole defects under uniform temperature changes were analyzed using a two-dimensional finite element method (FEM). Four kinds of adhesive butt joints which contained no hole, 3-hole, 8-hole, and 16-hole defects in the adhesive layer were studied. In particular, the stress concentrations around the hole defects and near the edges of the interface between the adherends and the adhesive were examined. From the results, the thermal stresses around the hole defects located near the center of the adhesive were found to be larger than those around the hole defects located near the free surface of the adhesive. The thermal stress near the edges of the interface decreased with an increase in the number of holes and a decrease in Young's modulus of the adhesive. For verification, photoelastic experiments were carried out and fairly good agreement was seen between the numerical and the experimental results.

A General Formulation of Stress Distribution in Cylinders Subjected to Non-Uniform External Pressure

This work presents a two-dimensional stress analysis for elastic solid cylinders subjected to combined loading. The loading is generally formed with a number of concentrated and partially distributed forces all applied radially on the outer surface. The distributed forces cause pressures with non-uniform intensity along the circumferential direction. The cylinder is assumed to be long so that a state of plane-strain is valid. To obtain the stress distribution for the problem of partially distributed forces a new approach is followed first introduced in this paper. It is based on the expressions formed after using the theory of simple radial stress distribution when point-forces are applied on the cylinder and leads to the solution after direct integration. The total stresses due to both concentrated and distributed forces are obtained using the method of superposition. Apart from its simplified formulation, this general solution is always preferable since it proved to have a great advantage. As a result of not containing Fourier series, it eliminates some problems of convergence of the series at the boundaries that appear due to the Gibbs phenomena when the boundary conditions are a discontinuous function. Numerical results are presented for some interesting cases of loading conditions.

The role of cuspal flexure in the development of abfraction lesions: a finite element study.

A tooth flexure mechanism has been proposed over the past 15 yr to explain non-carious cervical tooth loss. It is well established that cavity preparation weakens a tooth, resulting in more cuspal movement under occlusal load. The aim of this study was to investigate the effect that an occlusal restoration would have on the stress profile in the cervical region of a lower second premolar using two-dimensional finite element stress analysis. Under an eccentric 100 N occlusal load, a premolar with an occlusal amalgam restoration showed peak tensile and shear stresses in the buccal cervical region that were in excess of the known failure stress for enamel. Increases in the cavity depth of the occlusal amalgam restoration were found to increase cervical stress more than increases in cavity width. It was concluded that the weakening effect of cavity preparation may contribute to the development of non-carious cervical tooth loss.

Methods to improve a periodontally involved terminal abutment of a cantilever fixed partial denture - a finite element stress analysis

Journal of Oral RehabilitationVolume 25, Issue 4 p. 253-257 Methods to improve a periodontally involved terminal abutment of a cantilever fixed partial denture – a finite element stress analysis C. H. Wang, C. H. Wang Department of Prosthodontics, School of Dentistry andSearch for more papers by this authorH. E. Lee, H. E. Lee Department of Prosthodontics, School of Dentistry andSearch for more papers by this authorC. C. Wang, C. C. Wang Department of Prosthodontics, School of Dentistry andSearch for more papers by this authorH. P. Chang, H. P. Chang *Graduate Institute of Dental Sciences, Kaohsiung Medical College, Kaohsiung, TaiwanThe two-dimensional plane stress finite element stress analysis was used to evaluate the stress of mandibular posterior cantilevers for compromised periodontal involved distal terminal abutments. Some commonly practiced methods to alleviate the stress from mastication of the cantilever FPDs were also evaluated. From the analysis the following was concluded: (1) The most distal terminal abutment of a cantilever FPD generally experienced a high stress concentration. (2) The cantilever FPDs require at least two abutments. Optimum stress reduction occurred with a splinting of three abutments. To increase the number of abutments to more than three, would not result in a proportional and meaningful reduction of stress in the periodontium. (3) To alter the bridge material with more rigid material or to have a longer marginal preparation of the terminal abutment are ineffective for better stress distribution.Search for more papers by this author C. H. Wang, C. H. Wang Department of Prosthodontics, School of Dentistry andSearch for more papers by this authorH. E. Lee, H. E. Lee Department of Prosthodontics, School of Dentistry andSearch for more papers by this authorC. C. Wang, C. C. Wang Department of Prosthodontics, School of Dentistry andSearch for more papers by this authorH. P. Chang, H. P. Chang *Graduate Institute of Dental Sciences, Kaohsiung Medical College, Kaohsiung, TaiwanThe two-dimensional plane stress finite element stress analysis was used to evaluate the stress of mandibular posterior cantilevers for compromised periodontal involved distal terminal abutments. Some commonly practiced methods to alleviate the stress from mastication of the cantilever FPDs were also evaluated. From the analysis the following was concluded: (1) The most distal terminal abutment of a cantilever FPD generally experienced a high stress concentration. (2) The cantilever FPDs require at least two abutments. Optimum stress reduction occurred with a splinting of three abutments. To increase the number of abutments to more than three, would not result in a proportional and meaningful reduction of stress in the periodontium. (3) To alter the bridge material with more rigid material or to have a longer marginal preparation of the terminal abutment are ineffective for better stress distribution.Search for more papers by this author First published: 15 January 2004 https://doi.org/10.1111/j.1365-2842.1998.00234.xCitations: 12 Dr Chau-Hsiang Wang, School of Dentistry, Kaohsiung Medical College, 100, Shih-Chuen 1st Road, Kaohsiung 80708, Taiwan. Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume25, Issue4April 1998Pages 253-257 RelatedInformation

Methods to improve a periodontally involved terminal abutment of a cantilever fixed partial denture--a finite element stress analysis.

The two-dimensional plane stress finite element stress analysis was used to evaluate the stress of mandibular posterior cantilevers for compromised periodontal involved distal terminal abutments. Some commonly practiced methods to alleviate the stress from mastication of the cantilever FPDs were also evaluated. From the analysis the following was concluded: (1) The most distal terminal abutment of a cantilever FPD generally experienced a high stress concentration. (2) The cantilever FPDs require at least two abutments. Optimum stress reduction occurred with a splinting of three abutments. To increase the number of abutments to more than three, would not result in a proportional and meaningful reduction of stress in the periodontium. (3) To alter the bridge material with more rigid material or to have a longer marginal preparation of the terminal abutment are ineffective for better stress distribution.

A two-dimensional stress analysis of single-lap adhesive joints subjected to external bending moments

The stress distributions in single-lap adhesive joints of similar adherends subjected to external bending moments have been analyzed as a three-body contact problem using a two-dimensional theory of elasticity (plain strain state). In the analysis, both adherends and the adhesive were replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli of the adherends to that of the adhesive and the adhesive thickness on the stress distribution at the interfaces were examined. It was found that the stress singularity occurs at the edges of the interfaces and that the peel stress at the edges of the interfaces increases with decreasing Young's modulus of the adherends. It was noticed that the singular stress decreases at the edges of the interfaces as the adherend thickness increases. In addition, photoelastic experiments and FEM (finite element method) calculations were carried out and fairly good agreement was found between the analytical and the experimental results.

Adaptive mesh refinement for localised phenomena

The present work is concerned with the development, testing and use of finite element based methods in conjunction with adaptive mesh refinement procedures for the solution of three types of static and dynamic stress analysis problems. First, an adaptive mesh refinement procedure is introduced and used in static plate bending finite element analysis based on Mindlin-Reissner assumptions to study the edge effects which occur in plates with certain types of boundary conditions. Several issues of finite element mesh dependence and adaptivity in strain localisation problems are then discussed and illustrated. Finally, adaptive finite element methods for the solution of two-dimensional transient dynamic stress analysis problems are developed and tested on some benchmark examples. In all cases cited above there is a need to refine the finite element mesh locally in certain zones either within or at the boundary of the domain under consideration. In the transient dynamic analysis there is a further problem; these zones will move with time.

A two-dimensional stress analysis and strength evaluation of band adhesive butt joints subjected to tensile loads

The stresses in band adhesive butt joints, in which two adherends are bonded partially at the interfaces, are analyzed, using a two-dimensional theory of elasticity, in order to demonstrate the usefulness of the joints. In the analysis, similar adherends and adhesive bonds, which are bonded at two or three regions, are, respectively, replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli for adherends to that for adhesives, the adhesive thickness, the bonding area and position, and the load distribution are shown on the stress distributions at interfaces. It is seen that band adhesive joints are useful when the bonding area and positions are changed with external load distributions. Photoelastic experiments and the measurement of the adherend strains were carried out. The analytical results are in a fairly good agreement with the experimental results. In addition, a method for estimating the joint strength is proposed by using the interface stress distribution obtained by the analysis. Experiments concerning joint strength were performed and fairly good agreement is found between the estimated values and the experimental results.

Two-Dimensional Stress Analysis with Initial Strain by Improved Multiple-Reciprocity Boundary Element Method.

Linear stress analysis without initial strain can be easily carried out using the boundary element method. However, in general, domain integrals are necessary to solve the linear stress problem with initial strain. This paper shows that the two-dimensional linear stress problem with initial strain can be solved without the need for a domain integral. In this paper, the distribution of initial strain is interpolated using a boundary integral equation. A new computer program is developed and applied to simple problems.

Effect of the archwire slot profile on the performance of bonded orthodontic brackets

The finite element analysis method and a two-dimensional idealization were used to conduct a parametric study of the effect of the archwire slot (or insert) profile on the stresses in, deformation of, and efficiency of a model of a bonded edge-wise "combination-materials" type of orthodontic bracket. The results are consistent with a priori expectations and are qualitatively the same as those obtained by previous workers who used the two-dimensional photoelasticity stress analysis method. The results thus highlight a possible approach to improving the clinical performance of these brackets.

A two-dimensional stress analysis of single-lap adhesive joints subjected to tensile loads

The contact stress distributions between adherends and an adhesive and the deformation in single-lap adhesive joints subjected to tensile loads are analyzed as a three-body contact problem using a two-dimensional theory of elasticity. In the numerical calculations, the effects of the ratio of Young's moduli of the adherends to that of the adhesive, the adhesive thickness, and the lap length on the contact stress distributions at the interfaces are examined. As a result, it is found that the stress near the edges of the interfaces increases as Young's moduli of the adherends and the adherend thickness decrease. In addition, the contact stress distribution is analyzed by the finite-element method (FEM). Fairly good agreement is seen between the numerical results and the FEM results; however, a difference is seen between the numerical results and the results obtained by other researchers.

Identification of Peak Stresses in Cardiac Prostheses

This study assessed the accuracy of using a two-dimensional principal stress analysis compared to a three-dimensional analysis in estimating peak turbulent stresses in complex three-dimensional flows associated with cardiac prostheses. Three-component, coincident laser Doppler anemometer measurements were obtained in steady flow downstream of three prosthetic valves: a St. Jude bileaflet, Bjork-Shiley monostrut tilting disc, and Starr-Edwards ball and cage. Two-dimensional and three-dimensional principal stress analyses were performed to identify local peak stresses. Valves with locally two-dimensional flows exhibited a 10-15% underestimation of the largest measured normal stresses compared to the three-dimensional principal stresses. In nearly all flows, measured shear stresses underestimated peak principal shear stresses by 10-100%. Differences between the two-dimensional and three-dimensional principal stress analysis were less than 10% in locally two-dimensional flows. In three-dimensional flows, the two-dimensional principal stresses typically underestimated three-dimensional values by nearly 20%. However, the agreement of the two-dimensional principal stress with the three-dimensional principal stresses was dependent upon the two velocity-components used in the two-dimensional analysis, and was observed to vary across the valve flow field because of flow structure variation. The use of a two-dimensional principal stress analysis with two-component velocity data obtained from measurements misaligned with the plane of maximum mean flow shear can underpredict maximum shear stresses by as much as 100%.ASAIO Journal1996;42:154-163.

Two-Dimensional Stress Analysis of Single-Lap Joints of Dissimilar Adherends Subjected to External Bending Moments.

The stress distributions of single-lap adhesive joints of dissimilar adherends subjected to external bending moments are analyzed as a three-body contact problem using the two-dimensional theory of elasticity. In the analysis, dissimilar adherends and an adhesive are replaced by finite strips, respectively. In the numerical calculations, the effects of the ratio of Young's modulus, thickness and length of dissimilar adherends on the interface stress distributions are examined. As a result it is found that the stress singularity occurred near the edge of the interface and it increases at the edge of the interface of the adherend with greater Young's modulus. It is also seen that the singular stress decreases at the edge of the interface of the adherend with larger thickness. In addition, experiments are carried out and fairly good agreement is found between the analytical and the experimental results.