Two-dimensional Theory Of Elasticity Research Articles

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.

Analysis of interference fit pin joints subjected to bearing bypass loads

The composite plate is treated as an orthotropic laminate and the pin as a rigid circular disc, and a two-dimensional linear elasticity theory is used. The geometry considered is that of a rectangular plate with a single circular pin on one of the middle lines subjected to different loads uniformly distributed stresses on two opposite sides. The results highlight the nonlinear behavior of such a joint with load magnitude(s)

Design Optimization of a Prosthesis Stem Reinforcing Shell in Total Hip Arthroplasty

The use of a perforated, titanium funicular shell to support the proximal femoral cortex in total hip arthroplasty was evaluated with the aid of both analytical and numerical techniques. The principal interactions between the femoral cortex, the metal shell, the implant stem and the acrylic bone cement were modeled using beam on elastic foundations theory and two-dimensional elasticity theory. Subsequent formulation of this model as a nonlinear design optimization problem enabled the determination of the dimensions of the implant and reinforcing shell which minimized an objective function based on a simplified material failure criterion. Two cases were examined, each with two cervico-diaphyseal angles: case A: with a rigid contact between a proximal prosthesis collar and the calcar femorale and case B: no collar contact (a collarless prosthesis or post-operative loosening). Case A achieved an optimal solution at a stem diameter 11-23 percent of the cortex inner diameter, a stem length to diameter ratio of 12-40, shell diameter 22-53 percent and thickness 0.2-7.2 percent of the cortex inner diameter and thickness, respectively. Case B achieved an optimal solution at a stem diameter 67-92 percent of the cortex inner diameter, length to diameter ratio of 4-6, and no shell. In case A the collar support makes the type of internal fixation unimportant, while in the more realistic case B, the shell is not recommended.

Stress Distribution in Plane Scarf and Butt Joints

The stress distribution in a plane scarf joint, which may have an arbitrary angle of scarf as well as arbitrary elastic parameters for its adherends and adhesive, is analyzed. The analysis is based on the two-dimensional elasticity theory in conjunction with the variational principle of complementary energy. Minimizing the energy functional leads to a specific optimization problem with two variables for the determination of the stresses. Some typical features of the stress distribution are shown by numerical examples. Criteria for uniformly distributed adhesive stresses which are of importance in practice are deduced. The butt joint is treated as a special case of scarf joints.

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.

1スパン1層耐震壁についてフーリエ級数解を利用して求めるせん断型剛性と節点回転断性 : 耐震壁の節点剛性マトリックスに関する実用解 その2

This paper is a follow-up of the paper with the same subtitle in the previous Journal of Structural and Construction Engineering (Transactions of AIJ, No. 413, July, 1990). In this paper, a practical calculation method for the stiffness matrix elements, pertaining to the shear type stiffness and the rotational stiffness of the beam-to-column connections assumed to be rigid zone in elastic framed shear walls, is proposed. The shear type stiffness of framed shear walls without floor" slabs can not be evaluated satisfactorily by the I-beam solutions itself. Also, ' the rotational stiffness of the beam-to-column connections can not be evaluated by using I-beam theory. This is because the rotational stiffness of the connections is different from that of horizontal or vertical cross section of the shear wall. Therefore, the practical calculation charts based on the two-dimensional theory of elasticity are proposed in order to obtain the shear type -stiffness and the rotational stiffness of the connections with a high accuracy. These proposed stiffnesses will be adopted in the formulation of a practical nodal stiffness matrix of the framed shear walls together with the flexural and axial stiffnesses which were proposed in the previous paper. This practical nodal stiffness matrix will be useful in analyzing the elastic behaviour of the frame structures stiffened with shear walls by matrix method of structural analysis.

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.

A Study of Spur Gear Geometry Factor Through Complex Potential Analysis

Bending stresses in spur gears have been obtained analytically using the Complex Potential Method of the two-dimensional theory of elasticity and conformal mapping of the tooth profile. Effects of profile shift and sliding friction on geometry factor have been studied for 20 deg pressure angle and numbers of teeth ranging from 20 to 150. It has been shown how these results can be applied to obtain a geometry factor corrected to include either the profile or the coefficient of friction effect in a given gear pair.

Acoustic characteristics and the design of two-layered soundproof plates

This paper presents exact solutions for the coincidence frequency and the sound transmission loss of two-layered infinite plates excited by a plane acoustic wave. The problem is studied based on the two-dimensional elasticity theory with the use of the Lamé potential functions. A simple design method for a soundproof sheet with high transmission loss and high coincidence frequency is presented and illustrated with some examples. The results obtained are also compared with those from the thick plate theory.

Vibration analysis of thick rotating cylindrical shells based on the two-dimensional elasticity theory.

Vibration analysis of infinite thick rotating cylindrical shells is described on the basis of the two-dimensional elasticity theory. Starting from the state of plane strain, the basic equation in the steady rotating state, which is used to obtain the initial stresses, is derived from Hamilton's principle, and the frequency equation, including the effect of the initial stresses due to the rotation, is formulated by Ritz's method. The numerical results for the frequencies in the non-rotating and rotating state are compared with those based on Timoshenko type shell theory and the available range in the latter theory is examined about the thickness and rotating speed of a shell.

Vibration analysis of thick rotating cylindrical shells based on the two-dimensional elasticity theory.

Vibration analysis of infinite thick rotating cylindrical shells is described on the basis of the two-dimensional elasticity theory. Starting from the state of plane strain, the basic equation in the steady rotating state, which is used to obtain the initial stresses, is derived from Hamilton's principle, and the frequency equation, including the effect of the initial stresses due to the rotation, is formulated by Ritz's method. The numerical results for the frequencies in the non-rotating stare are compared with those based on Timoshenko-type shell theory and the available range in the latter theory is examined in terms of the thickness and rotating speed of a shell.

Two-dimensional stress analysis of adhesive butt joint subjected to external bending moments. (The case where adherends are dissimilar materials).

In the present paper, the stresses of butt adhesive joints are analyzed by a two-dimensional theory of elasticity in order to establish the fracture criteria when dissimilar adherends are bonded by an adhesive. Dissimilar adherends and an adhesive are replaced with finite strips, respectively, and the analyses are done as a three body contact problem. In numerical computations, the effects of the ratio of Young's modulus of dissimilar adherends, the ratio of Young's modulus of adherends to that of an adhesive and the thickness of the adhesives are shown on the distributions at the interfaces of the joints. As a result, it is seen that the principal stress becomes maximum at the interface between the adhesive and the adherend having high Young's modulus. For verification, experiments are performed. Analytical results are in fairly good agreement with experimental ones.

A Two-Dimensional Stress Analysis of Butt Adhesive Joints Having a Circular Hole in the Adhesive : (The Case Where Joints are Subjected to External tensile Loads)

Stress distribution and tensile strength were examined when a butt adhesive joint having a circular hole defect in an adhesive was subjected to an external tensile load. In the analyses, general representations of the stresses and the displacements were given using the two-dimensional theory of elasticity. The effects of the location and the size of a hole on the stress distribution were clarified by numerical computations. Then, comparing the principal stress at the periphery of a hole with that of the interface between an adherend and an adhesive, discussion was made on the strength of the joint. It was seen that the stress concentration increase with a decrease in hole size, the change being dependent on the position of the hole. For verification, photoelastic experiments were performed and analytical results were in fairly good agreement with the experimental ones.

Stress Analysis ofT-type Butt Adhesive Joint Subjected to External Bending Moments

Abstract Stress distributions and displacements at the interface between an adhesive and an adherend are examined when a T-type butt adhesive joint, in which two thin plates are joined, is subjected to an external bending moment. In the analyses, general representations of the stresses and the displacements are given using a two-dimensional theory of elasticity in the case where two dissimilar plates are joined. Next, in the case of plates with the same material, effects of Young's modulus of plates to that of an adhesive and the thickness of the adhesive on the stress distribution are made clear by numerical computations. For verification, experiments are performed and an analytical result is in a fairly good agreement with an experimental one.

Stress Analysis of a Spinning Annular Disk to a Stationary Distributed, In-Plane Edge Load

In-plane stress distribution in a spinning annular disk is studied analytically. The disk is clamped at the inner boundary and subjected to a stationary distributed load along the outer boundary. The solution is determined through a Galilean transformation by using the Lame´ potential functions and the two-dimensional elasticity theory. Numerical results are presented for WA vitrified grinding wheels with outer radii of 50 mm and inner radii of 25 mm rotating at 3000 rpm and 15000 rpm.

Stress analysis of a viscoelastic solid of arbitrary cylindrical shape having a circular cavity and subject to internal vibration pressures

This paper is concerned with a method for solving stress problems of a viscoelastic solid of arbitrary shape with a circular cavity subjected to a vibration pressure along the cavity. In the analysis the exact solutions which satisfy the boundary conditions along the cavity have been derived from the equations of motion of elastic solids based on the two-dimensional theory of elasticity. The boundary conditions along the outer surface of arbitrary shape have been satisfied by means of the Fourier expansion collocation method. The analysis takes account of the viscoelasticity and the structural damping theory is used. As examples, stresses in the solids of circular, hexagonal, square, elliptical and truncated elliptical shapes have been calculated, and curves for the forced vibration response are presented.

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

This paper deals with a two-dimensional stress analysis of adhesive butt joints subjected to tear loads. The purpose of the present paper is to contribute to an establishment of the fracture criteria of joints. Similar adherends and an adhesive bond are replaced with finite strips in the analysis. Stress distributions in adhesive joints are analyzed by using the two-dimensional theory of elasticity. The effects of the ratio of Young's modulus of adherends to that of the adhesive and the thickness of adhesive bonds on the stress distributions are shown by numerical computations. For verification, experiments are performed with respect to the strain of adherends. The analytical results are in fairly good agreement with the experimental ones.

The characteristics of bolted joints with tap bolts subjected to external bending moments. (The case where a clamped part is T-flange with a full face metallic gasket or a filler plate)

Few investigations have been carried out on the characteristic of a bolted joint with tap bolts subjected to external bending moments. In this paper, the characteristics of a T-flange connection with tap bolts, including a full face metallic gasket or a filler plate, are examined. For analysis, a T-flange, gasket (filler plate) and base were replaced with finite strips. Contact stress distribution, the force ratio for the external bending moment (the relationship between an increment (decrement) of the bolt axial force and the external bending moment) and the maximum stress produced in the bolts are analyzed using a two-dimensional theory of elasticity. Furthermore, the characteristics of a circular flange connection are estimated by using the two-dimensional model. For verification, experiments were performed with respect to the force ratio for the external bending moment, contact stress distribution and the maximum stress in the bolt. Analytical results are in fairly good agreement with experimental ones.