Equilibrium of a Prestressed Strip Reinforced with Elastic Plates

The contact problem for a prestressed elastic strip reinforced with equally spaced elastic plates is considered. The Fourier integral transform is used to construct an influence function of a unit concentrated force acting on the infinite elastic strip with one edge constrained. The transmission of forces from the thin elastic plates to the prestressed strip is analyzed. On the assumption that the beam bending model and the uniaxial stress model are valid for an elastic plate subjected to both vertical and horizontal forces, the problem is mathematically formulated as a system of integro-differential equations for unknown contact stresses. This system is reduced to an infinite system of algebraic equations solved by the reduction method. The effect of the initial stresses on the distribution of contact forces in the strip under tension and compression is studied     

Temperature and thermal stresses in material of a pad during braking

The transient temperature field and corresponding quasi-static thermal stresses are analysed in a system consisting of a semi-space and a strip. The strip is heated on its outer surface by a heat flux with the intensity equal to the specific power of friction during braking with a uniform retardation. The evolution and distribution in depth from a surface of friction for temperatures and thermal stresses were investigated for the metal-ceramic FMK-11 material of the strip.     

Stresses in a quasi-isotropic pin-loaded connector using photoelasticity

Birefringent glass-epoxy and a numerical stress-separation scheme are used to compute the stresses in the vicinity of a pin-loaded hole. The radial and circumferential stresses at the hole edge, and the net-section and shear-out stresses are computed. The numerical and experimental results of other investigators are compared with the computed stresses. The fixture used to load the connector is discussed and typical isochromatic- and isoclinic-fringe patterns are presented. The stress-separation scheme is briefly described.     

Stress distributions in a semi-infinite plate due to a pin determined by interferometric method

The stress distributions in a semi-infinite plate due to a loaded pin of the same material as the plate are systematically investigated by an interferometric method which has been developed by the authors. For the experiments, a finite plate of diallylphthalate with a circular hole is used. It is supported at one side and loaded in the direction normal to the opposing straight edge by a pin which just fits the hole. The ratio of the distancee between the hole center and the straight edge to the diameterd of the hole is varied in steps from 4.0 to 1.0. At each step, the distributions of principal stresses σ₁ and σ₂ along the hole edge, line of symmetry and straight edge, which have not been fully investigated especially whene/d is small, are obtained separately from the isopachic and isochromatic fringes of the interfero-stress patterns. The relations between the maximum values of these stresses and the shape factore/d are determined.     

Maximum stress in a tensile strip with a large hole

Measurements were made to decide between two solutions of the title problem. In question was the limiting value of the stress-concentration factor at the edge of a large hole in a tensile strip as the hole diameter approached the strip width. The results indicate that the stress-concentration factor is near two and support one of the solutions with a minor qualification.     

Hybrid stress analysis of perforated composites using strain gages

A strain gage hybrid method is described for determining individual stresses on the boundary and in the neighborhood of cutouts in orthotropic composites. Results agree with independent measurements and finite element analysis. Few measured strain data are needed, and the measured strains originate away from the hole. Ability to determine the stresses on the edge of a cutout from nonboundary measurements recognizes the difficulties in obtaining reliable measurements very near an edge while circumventing the challenge of attempting to bond gages to the transverse curved surface of a small hole or notch. The method also alleviates the problem of not knowing a priori where the most serious stress will occur on the geometric boundary and, hence, where to locate strain gages.     

Stresses around pin-loaded hole in composite laminates using direct boundary element method

This study is concerned with stresses around a pin-loaded hole in symmetrically stacked composite laminates of finite size using a two-dimensional direct boundary element method. Effects of friction and clearance between the pin and hole edge on the stresses are accounted for. Also geometric compatibility and force constraint between the pin and the plate are enforced. A new relation for geometric compatibility is proposed. Stress distributions and the contact angle with slip and no-slip regions around the pin-loaded hole corresponding to various parameters are investigated. Some interesting results are obtained. The present method is effective and simple to use which can be implemented with a personal computer.     

Investigation of stress-concentration factors in tensile strips

A photoelastic and a numerical investigation has been carried out to determine the stress-concentration factors at the edge of a central circular hole in a tensile strip for different ratios of hole diameter to width of the strip. The photoelastic data and the numerical results indicate that the stress-concentration factor at the minimum cross-sectional area tends to a value of two if the ratio of the hole diameter to the strip-width approaches a value of one.     

Stress intensity factors for an edge interface crack in a bonded semi-infinite plate for arbitrary material combination

Although a lot of interface crack problems were previously treated, few solutions are available under arbitrary crack lengths and material combinations. In this paper the stress intensity factors of an edge interface crack in a bonded strip are considered under tension with varying the crack length and material combinations systematically. Then, the limiting solutions are provided for an edge interface crack in a bonded semi-infinite plate under arbitrary material combinations. In order to calculate the stress intensity factors accurately, exact solutions in an infinite bonded plate are also considered to produce proportional singular stress fields in the analysis of FEM by superposing specific tensile and shear stresses at infinity. The details of this new numerical solution are described with clarifying the effect of the element size on the stress intensity factor. It is found that for the edge interface crack the normalized stress intensity factors are not always finite depending upon Dunders’ parameters. This behavior can be explained from the condition of the singular stress at the end of bonded strip. Convenient formulas are also given by fitting the computed results.     

Stress intensity factors for three-dimensional cracks in functionally graded materials using enriched finite elements

A three-dimensional enriched finite-element methodology is presented to compute stress intensity factors for three-dimensional cracks contained in functionally graded materials (FGMs). A general-purpose 3D finite-element based fracture analysis program, FRAC3D, is enhanced to include this capability. First, using available solutions from the literature, comparisons have been made in terms of stresses under different loading conditions, such as uniform tensile, bending and thermal loads. Mesh refinement studies are also performed. The fracture solutions are obtained for edge cracks in an FGM strip and surface cracks in a finite-thickness FGM plate and compared with existing solutions in the literature. Further analyses are performed to study the behavior of stress intensity factor near the free surface where crack front terminates. It is shown that three-dimensional enriched finite elements provide accurate and efficient fracture solutions for three-dimensional cracks contained in functionally graded materials.     

On the solution singularity in the plane elasticity problem for a cantilever strip

The plane elasticity problem of bending of a cantilever strip whose material is assumed to be incompressible in the transverse direction is solved. It is shown that, in the classical statement of of the boundary condition for the fixed edge of the strip, the solution has a singularity at the corner points of the edge. Several cases of the strip fixation and loading characterized by the presence or absence of the solution singularity are considered. The strength of glass beams of three types, for which the theory of elasticity predicts whether the normal stress has a singularity, is studied experimentally. It is shown that the limit stresses for the beams of the types under study are practically the same, which testifies that the solution singularity does not have any physical nature.     

Photothermoelastic investigation of stresses around a hole in a plate subjected to thermal shock

This paper contains a three-dimensional photothermoelastic study of stresses generated around the edge of a hole in a flat unrestrained plate subjected to a thermal shock uniformly applied to one face of the plate. The approach taken is experimental in nature, utilizing a newly developed three-dimensional, non-destructive photoelastic technique. An extrapolation procedure is formulated in order to determine transient fringe orders at the thermally shocked surface. For the case considered, the thermal-stress-concentration factor at the edge of the hole was found to be 1.28. Paper was presented at 1964 SESA Annual Meeting held in Cleveland, Ohio, on October 28–30. Work reported herein was conducted by the Douglas Missile and Space Systems Division under company sponsored Research and Development funds.     

Thermoelastic Determination of Individual Stresses in Vicinity of a Near-Edge Hole Beneath a Concentrated Load

Thermoelastic data are combined with an Airy stress function to determine the individual stresses on and near the boundary of a circular hole which is located below a concentrated edge-load in a plate. Coefficients of the stress function are evaluated from the measured temperatures and the local traction-free conditions are satisfied by imposing s_rr = t_rq = 0 {\sigma_{r{\rm{r}}}} = {\tau_{r\theta }} = 0 analytically on the edge of the hole. The latter has the advantage of reducing the number of coefficients in the stress function series. The method simultaneously smoothes the measured input data, satisfies the local boundary conditions and evaluates individual stresses on, and in the neighbourhood of, the edge of the hole. Attention is paid to how many coefficients to retain in the stress function series. Although the presence of high stress concentration factors, together with a hole-diameter-to-plate-thickness ratio of only two, result in some three-dimensional effects, these are relatively small and the agreement between the thermoelastic values, those from recorded strains and FEM-predicted surface stresses is good.     

Convective cooling/heating induced thermal stresses in a fluid saturated porous medium undergoing local thermal non-equilibrium

Local thermal non-equilibrium (LTNE) may have profound effects on the pore pressure and thermal stresses in fluid saturated porous media under transient thermal loads. This work investigates the temperature, pore pressure, and thermal stress distributions in a porous medium subjected to convective cooling/heating on its boundary. The LTNE thermo-poroelasticity equations are solved by means of Laplace transform for two fundamental problems in petroleum engineering and nuclear waste storage applications, i.e., an infinite porous medium containing a cylindrical hole or a spherical cavity subjected to symmetrical thermo-mechanical loads on the cavity boundary. Numerical examples are presented to examine the effects of LTNE under convective cooling/heating conditions on the temperature, pore pressure and thermal stresses around the cavities. The results show that the LTNE effects become more pronounced when the convective heat transfer boundary conditions are employed. For the cylindrical hole problem of a sandstone formation, the thermally induced pore pressure and the magnitude of thermal stresses are significantly higher than the corresponding values in the classical poroelasticity, which is particularly true under convective cooling with moderate Biot numbers. For the spherical cavity problem of a clay medium, the LTNE effect may become significant depending on the boundary conditions employed in the classical theory.     

Hybrid Thermoelastic Stress Analysis of a Pinned Joint

Mechanical joints such as bolted or pinned connections are commonly used to fasten mechanical or structural members together. Inadequate knowledge of the stresses at the edge of the loaded holes can render it difficult to stress analyze such mechanical fasteners theoretically or numerically. Thermoelastic stress analysis (TSA) is utilized here to analyze a plane-stressed pin-loaded plate. The approach combines the recorded temperature information with an Airy stress function, plus imposes the traction-free conditions on the non-contacting edge of the hole and on the external boundaries of the plate. Individual components of stress are determined full-field as well as on the pin-plate interface. In addition to agreeing with the frequently assumed interface contact stresses in mechanical connections having zero clearance, the TSA results satisfy force equilibrium, are compatible with residual markings on the contacted surfaces of the pin and the hole, and correlate with FEM predictions. Significant advantages of TSA here include neither needing to know the elastic modulus nor to differentiate the recorded information.     

A Prestressed Elastic Strip with Elastic Reinforcements

A contact problem is studied for a prestressed elastic strip with an elastic reinforcement. The integral Fourier transform is used to construct an influence function for an infinite strip with one face fixed. A unit concentrated force is applied to the strip at an arbitrary angle. The contact problem on force transfer from a thin infinite stringer to the prestressed strip is solved. The problem is mathematically formulated as a system of integro-differential equations for the unknown contact stresses on the assumption that the beam bending model and the uniaxial stress model are valid for the stringer, which is subjected to both vertical and horizontal forces. This system is solved in a closed form using the integral Fourier transform. The contact stresses are expressed in terms of Fourier integrals in a quite simple form. The influence of the initial stresses on the contact stress distribution is analyzed, and effects of concentrated load are revealed     

Multiple crack propagation in a strip caused by thermal shock

The time-dependent stress intensities due to quenching are calculated by the boundary element method for an array of parallel and equal spaced edge cracks in a long strip. Analyzed is the sequence of crack pattern formation. The predicted patterns have essential features in common with the experimental ones. This tends to support a recently developed approach for analyzing single and multiple crack growth under thermal shock.     

Fracture assessment of PMMA/Si kitchen sinks made from acrylic casting dispersion

Acrylic casting dispersion is used to fabricate kitchen sinks made of PMMA/Si which stands for poly-methyl methacrylate mixed with a fine dispersion of silica. The composite is suited for sanitary wares that are subjected to severe temperatures, giving rise to high thermal stresses. This leads to failure by cracking in the region near the drain hole. Such conditions are investigated by determining the mechanical and fracture properties for two different chemical compositions of PMMA. They are referred to by trade marks from ICI as Asterite and Amatis. Data are obtained for temperatures from 0 to 95 °. Extensometry data are also obtained to the thermal stresses around the drain hole subjected to alternating flow of cold and hot water. Critical crack lengths are determined from the critical stress intensity factor and maximum local tensile stresses based on measured data. They are estimated to be 1.5 mm and 4.0 mm, respectively, for the Asterite and Amatis composites. These results confirm with practice where the cracking of the former was observed while the latter did not crack.     

十次对称二维准晶中的热应力分析

推导了当考虑热效应时十次对称二维准晶体平面应变问题的通解表示．作为应用，采用所获得的通解首先得到了十次对称二维准晶体中的一个点热源所引起的声子场和相位子场，给出了点热源所引起的声子场和相位子场应力分量的解析表达式；接着获得了在均匀热流作用下十次对称二维准晶体中-绝缘椭圆孔洞所引起的热应力问题的弹性解答，给出了沿椭圆边界环向应力分布的解析表达式；当椭圆的短轴趋于零时，则获得了裂纹问题的解答，给出了应力强度因子、裂纹表面张开位移及能量释放率的解析表达式；推导了在任意热载荷作用下裂尖附近的渐近场．     

A multidimensional-crack-growth prediction methodology for flaws originating at fastener holes

A multidimensional-crack-growth prediction methodology for flawed fastener holes is described. The methodology uses a slice-synthesis model of the flawed hole for predicting the crack-driving force around the periphery after each increment of advance. Analytic predictions of the crack-growth rate are compared with test results for various examples. It is shown that residual stresses due to yielding at the hole edge and the cycle-by-cycle shape changes are a major cause of apparent crack-growth retardation or acceleration, and that the assumption of a constant shape, as is a common practice, can lead to highly misleading estimates of service life.