A large orthotropic plate with misfit pin under arbitrarily oriented biaxial loading

The problem of misfit (interference or clearance) pin in a large orthotropic plate was solved earlier by the authors for biaxial loading in the principal directions of orthotropy. Here, a more general case of arbitrarily oriented loading is considered. The most important aspect of the problem studied is the partial contact at the pin-hole interface. The solution is obtained by extending the use of ‘inverse technique’ which was successfully applied earlier by the authors to problems of pins in isotropic and orthotropic domains. The loss of symmetry because of the arbitrary orientation of loading makes the problem more complex. Additional parameters are then involved in the inversion of the problem for the solution. Numerical results are presented primarily for a smooth interference fit pin in a typical orthotropic plate.     

Stress and strength analysis of pin joints in laminated anisotropic plates

Mechanical joints in composites can be tailored to achieve improved performance and better life by appropriately selecting the laminate parameters. In order to gain the best advantage of this possibility of tailoring the laminate, it is necessary to understand the influence of laminate parameters on the behaviour of joints in composites. Most of the earlier studies in this direction were based on simplified assumptions regarding load transfer at the pin-plate interface and such studies were only carried out on orthotropic and quasi-isotropic laminates. In the present study, a more rigorous analysis is carried out to study pin joints in laminates with anisotropic properties. Two types of laminates with (0/ + ₄/90)_s and (0/ ± ₂/90)_s layups made out of graphite epoxy T300/5208 material system are considered. The analysis mainly concentrates on clearance fit in which the pin is of smaller diameter compared to the hole. The main aspect of the analysis of pin joints is the changing contact between the pin and the plate with increasing load levels. The analysis is carried out by an iterative finite element technique and a computationally efficient routine is developed for this purpose. Numerical studies indicate that the location and magnitude of the peak stresses along the hole boundary are functions of fibre angle and the overall anisotropic properties. It is also shown that the conventional assumption of cosine distribution for the contact pressure between pin and the plate in the analysis lead to underestimation of bearing failure load and overestimation of shear and tensile failure loads in typical (0/90₅)_s cross-ply laminates.     

A BEM-based meshless solution to buckling and vibration problems of orthotropicplates

In this paper a BEM-based meshless solution is presented to buckling and vibration problems of Kirchhoff orthotropic plates with arbitrary shape. The plate is subjected to compressive centrally applied load together with arbitrarily transverse distributed or concentrated loading, while its edges are restrained by the most general linear boundary conditions. The resulting buckling and vibration problems are described by partial differential equations in terms of the deflection. Both problems are solved employing the Analog Equation Method (AEM). According to this method the fourth-order partial differential equation describing the response of the orthotropic plate is converted to an equivalent linear problem for an isotropic plate subjected only to a fictitious load under the same boundary conditions. The AEM is applied to the problem at hand as a boundary-only method by approximating the fictitious load with a radial basis function series. Thus, the method retains all the advantages of the pure BEM using a known simple fundamental solution. Example problems are presented for orthotropic plates, subjected to compressive or vibratory loading, to illustrate the method and demonstrate its efficiency and its accuracy.     

On the influence of clearance in orthotropic disc-pin contacts

Solutions to contact problems are important in mechanical as well as in civil engineering, and even for the most simple problems there is still a need for research results. In the present paper we use an alternative super element procedure to solve directly, without iteration and incrementation, an orthotropic disc-pin contact problem.

The most simple solutions are named Hertz solutions (from 1882), and we use one of these solutions for comparison with finite element results. As a function of the total contact force we find (inversely) the size of the contact area, the distribution of the contact pressure, and the contact compliance. In models of finite size the compliance depends on the flexibility of the total model, including the boundary condition of the model, and therefore disagreement with the locally based analytical models is expected.

The examples of an earlier paper were restricted to axisymmetric problems with isotropic, elastic materials and excluding friction. In the present paper we restrict to the two-dimensional problems of conforming cylindrical contact with focus on the orthotropic disc-pin contact where the hole is in an orthotropic disc, i.e., in a non-isotropic material. Especially the indentation (penetration, normal approach) is badly estimated by the analytical methods and therefore deserves special attention. Results from a number of parameter studies of the influence of clearance is presented, and from this follows that some almost linear relations are found. It is concluded that a simple analytical Hertz formula is useful, but it cannot give detailed information.     

Stability of laminated orthotropic plates upon slippage of layers

The article deals with a laminated orthotropic plate. Between the layers there is rigid contact as well as contact with frictionless slippage. On the end faces at the level of the neutral surface of the slipping layers the plate is loaded by tangential loads. The model of loss of stability is based on the hypotheses on displacements of the plate that take transverse shear strain into account. Normal displacements of the plate do not depend on the transverse coordinate. The hypotheses derived by iteration make it possible to satisfy the conditions of interlaminar contact, both rigid and with frictionless slippage, with respect to displacements and stresses, and also the conditions on the outer surfaces of the plate. With the aid of Lagrange's variational principle we obtained differential equations under conditions of the precritical and the postcritical state, and also the corresponding boundary conditions. The equations of the postcritical state are written in terms of displacements. On the basis of the presented equations the problem of the stability of a homogeneous orthotropic rectangular plate with pin support along the periphery is solved. It is shown that the results obtained with the suggested model coincide with the known results. The article also examines a square three-layered orthotropic plate under conditions of frictionless slippage contact between the layers and pin support along the periphery. The central layer is loaded by tangential loads on the end faces at the level of its neutral surface. It is shown that when slippage is taken into account, the critical forces are substantially reduced.Translated from Problemy Prochnosti, No. 8, pp. 35–41, August, 1994.     

Fatigue crack growth and life prediction of a single interference fitted holed plate

To understand the different aspects of fatigue behaviour of complex structural joints it will be much helpful if the effects of different parameters are studied separately. In this article, to study the isolated effect of interference fit on fatigue life a pined hole specimen is investigated. This specimen is a single‐holed plate with an oversized pin which force fitted to the hole. The investigation was carried out both experimentally and numerically. In the experimental part, interference fitted specimens along with open hole specimens were fatigue tested to study the experimental effect of the interference fit. In the numerical part, three‐dimensional finite element (FE) simulations have been performed in order to obtain the created stresses due to interference fit and subsequent applied longitudinal load at the holed plate. The stress distribution obtained from FE simulation around the hole was used to predict crack initiation life using Smith–Watson–Topper method and fatigue crack growth life using the NASGRO equation with applying the AFGROW computer code. The predicted fatigue life obtained from the numerical methods show a good agreement with the experimental fatigue life.     

Investigation on thermomechanical behavior of a HSLA steel circular plate under impact load

Based on the von Karman equation and classical thin plate theory, thermomechanical behavior of a high strength low alloy (HSLA) steel circular plate under impact load is investigated. Firstly, when the HSLA steel circular plate is impacted by a rigid impactor, the relation of the contact radius and the instantaneous relative displacement is obtained by using the modified nonlinear Hertzian contact law, and the contact force is solved by using the time increment method. Secondly, the nonlinear governing equations in the form of displacements for the HSLA steel circular plate under the impact load are obtained by using the Hamilton variational principle. Finally, the unknown variable functions are discretized in space and time domains by utilizing the finite difference method and Newmark method, and the whole problem is solved by the iterative method. Numerical results denote that the geometrical parameters, boundary conditions of the HSLA steel circular plate and the initial velocity of impactor have great influences on deformation, the contact force and stresses of the HSLA steel circular plate.     

Effect of the clearance and interference-fit on failure of the pin-loaded composites

The aim of this study is to examine the effect of the clearance and interference-fit on the failure mode, failure load and bearing strength of the pin-loaded joints subjected to traction forces. The failure load and failure mode are determined both experimentally and numerically. Three-dimensional finite element models are created using ANSYS software. Non-linear contact analyses are performed to examine the effects of the clearance and interference for different ratios of the edge distance-to-hole diameter (E/D) and plate width-to-hole diameter (W/D). Damage is also examined using scanning electron microscope (SEM). It is observed that interference for all pin-loaded joint configurations is beneficial. A good agreement between experimental and numerical results is obtained.     

配合方式对复合材料单钉单剪螺栓连接接头刚度的影响及其机制

针对单钉单剪复合材料螺栓连接,研究了间隙与干涉2种配合方式对接头刚度的影响及其机制。通过与试验结果的对比,验证了所采用的有限元方法的有效性。结果表明:对于复合材料单钉单剪螺栓连接,间隙配合导致接头刚度变小, 3%钉直径的间隙量导致接头刚度下降16%~17%,并且随着间隙量的增大,接头刚度基本呈线性下降;而对于装配过程中没有产生孔边分层损伤的干涉配合连接件, 0.5%钉直径的干涉量使得接头刚度增加了约15%。配合方式不同,连接件孔周接触应力峰值方向及厚度方向接触应力分布不均匀的程度不同,进而影响了接头刚度。      

Fracture mechanics deliberation of lugs

Mode I stress intensity factors for a symmetrical lug with a through radial crack emanating from the internal boundary were evaluated with finite element techniques. A new geometric configuration was developed which saves a minimum of 60% in computer time over the traditional configuration. The effect of interference fit and slip fit was investigated by comparing the results obtained for two different loading conditions; point force and uniform bearing pressure distribution, of which, pin loading yields the larger stress intensity factor. A means of estimating the residual life is also presented.     

Delamination buckling of laminated plates

The subject of this paper is the buckling of laminated plates, with a pre-existing delamination, subjected to in-plane loading. Each laminate is modelled as an orthotropic Mindlin plate. The analysis is carried out by a combination of the finite element and asymptotic expansion methods. By applying the finite element method, plates with general delamination regions can be studied. The asymptotic expansion method reduces the number of unknown variables of the eigenvalue equation to that of the equation for a single Kirchhoff plate. Numerical results for the critical buckling load are presented for several examples. The effects of the shape, size and position of the delamination on the buckling load are studied through these examples.     

Magnetoelastodynamic stress and perturbation of magnetic field vector in an orthotropic laminated hollow cylinder

An analytical method is presented to solve magneto-elastic wave propagation and perturbation of the magnetic field vector in an orthotropic laminated hollow cylinder with arbitrary thickness. The magnetoelastodynamic equation for each separate orthotropic hollow cylinder is solved by making use of finite Hankel transforms and Laplace transforms. The unknown constants involved in the solution for each separate layer are determined by using the interface continuity conditions between layers and the boundary conditions at the internal and external boundaries of the laminated hollow cylinders. Thus, an exact solution for magnetoelastodynamic stresses and perturbation response of an axial magnetic field vector in laminated hollow cylinder is obtained. From sample numerical calculations, it is seen that the present method is suitable to solve magnetoelastodynamic problems of laminated hollow cylinders subjected to a radial shock load and an axial magnetic field.     

A finite element method for contact problems related to fracture mechanics

A finite element method for contact problems in crack mechanics is developed on the basis of the penalty function method. The method is successfully applied to three important problems in fracture mechanics: a crack propagated from a pin hole, a two-point supported specimen with an edge crack loaded by a stamp, and a thick plate with a through-wall crack under bending force.     

An elastostatic FEM/BEM analysis of vertically loaded raft and piled raft foundation

In this paper, a static analysis of vertically loaded raft and piled raft foundations in smooth and continuous contact with the supporting soil is presented. In this approach the finite element method (FEM) and the boundary element method (BEM) are coupled: the bending plate is assumed to have linear elastic properties and is modelled by FEM while the soil is considered as an elastic half-space in the BEM. The pile is represented by a single element and the shear force along the shaft is interpolated by a quadratic function. The plate–soil interface is divided into triangular boundary elements (soil) also called cells and finite elements (plate) and the subgrade reaction is linearly interpolated across each cell. The subgrade tractions are eliminated from the FEM and BEM algebraic systems of equations, resulting in the governing system of equations for plate–pile–soil interaction problems. Numerical results are presented and they are close to those resulting from much more elaborate analyses.     

子午线轮胎静负荷实验的有限元模拟

建立了一种子午线轮胎的三维非线性有限元模型,来模拟子午线轮胎的静负荷试验。模型中考虑了橡胶材料的非线性和不可压缩性、帘线-橡胶复合材料的各向异性、轮胎大变形导致的几何非线性以及轮胎与轮辋、轮胎与路面的接触非线性边界条件。提出了一种单元重叠技术,通过重叠不可压缩橡胶单元和描述帘线的单元来模拟帘线-橡胶复合材料,这种单元重叠技术产生的轮胎模型比正交各向异性模型计算过程更稳定。通过有限元分析,得到了子午线轮胎在充气压力和静负荷作用下的变形和应力分布情况以及接地区的压力分布情况,并将计算结果与试验结果进行了比较,两者吻合得很好。     

Torque transmission capability of composite–metal interference fit joints

In this paper the performance of an interference fit joint between a composite tube and a steel shaft under torsional load was investigated. Some important design parameters on the interference fit joint were presented and addressed based on the results from analytical and numerical models. The stress state of the joint under torsional load with contact elements was calculated by three dimensional finite element analysis. For the long term use of the interference joint the viscoelastic behavior of the composite tube was also considered through the analytical model. Finally the validity of analysis of the interference fit joint was experimentally examined.     

制造公差对复合材料螺栓连接结构强度分散性的影响

为解决由于螺栓和复合材料板制孔制造过程中不可避免的制造公差引起的配合间隙的不同,而使复合材料螺栓连接钉载分配不同,从而导致螺栓连接强度分散性的问题,以英制高锁螺栓和孔板制孔的制造公差为例,研究不同配合间隙下双剪四钉螺栓连接钉载分配情况,并进一步采用改进的特征曲线法、改进的强度包线法和渐进损伤模型对螺栓连接结构的强度进行预测,得到四钉连接失效强度的分散区间分别为[-3.87%,2.16%]、[-4.01%,3.95%]和[-3.16%,5.14%]。结果说明如果紧固件及螺栓孔均符合制造标准,则其对强度的影响范围不超过6%。     

Buckling analysis of orthotropic thin rectangular plates subjected to nonlinear in-plane distributed loads using generalized differential quadrature method

In the present work, buckling analysis of orthotropic thin rectangular plates with uniform thickness resting on Pasternak foundation are investigated for eight types of boundary conditions: SSSS, CCCC, SCSC, SSSC, SSCC, CCCF, SSFC, and CFCF. Based on classical plate theory, governing differential equation in buckling are solved numerically using generalized differential quadrature method (GDQM) to obtain critical buckling loads and corresponding modes. The kinds of nonlinear loading are presented in six cases including symmetrical and unsymmetrical distribution. In addition, the effects of aspect ratio, orthotropic moduli ratio and coefficients of foundation on the buckling load are illustrated. The present work is the first attempt to consider the influence of the nonlinearity of distributed in-plane bi-directional loading in determination of buckling load and representation of the corresponding shape modes. Some numerical examples are provided to demonstrate good accuracy of the GDQ method to evaluate the critical buckling load in case of nonlinear distributed bi-directional compressive loads. As shown, profile of distributed in-plane loading plays an important role on buckling behavior of the rectangular plate.     

Stress distributions in multi-fastened composite plates

This paper presents an analytical study of the stress distributions in pinjointed multi-fastened composite laminates. The finite element models which treat the pin and hole contact problem using a complete contact stress analysis are described. The condition of a perfect fit between the pin and hole, without lateral constraints, was applied. Membrane analysis has been utilised in conjunction with gap elements and friction for accurate modelling of the contact stresses and the stress distribution in the vicinity of the hole boundary. The accuracy of the analytical procedure, for two deformable bodies in contact, is confirmed by comparison with previous published work. The results show that the number of pins, pitch distance, number of rows, row spacing and hole pattern have a significant influence on joint performance.     

Stress intensity factors in finite orthotropic plates with a crack under mixed mode deformation

Mixed mode fracture problem is analyzed for the finite orthotropic plate where an inclined crack parallel to the fibre direction is centrally placed. Modified mapping collocation method with both uniform stress and uniform displacement boundary conditions is utilized to calculate stress intensity correction factors for glass/ epoxy and graphite/epoxy composites. Computed results are presented for selected combinations of crack length to width ratio L/W and plate aspect ratio H/W with various fibre orientations.