Jianqiao Ye

Three-dimensional vibration of laminated cylinders and cylindrical panels with symmetric or antisymmetric cross-ply lay-up

A refined formulation of an approach suitable for three-dimensional vibration analyses of homogeneous and cross-ply laminated cylinders and cylindrical panels (Soldatos and Hadjigeorgiou, 1990, J. Sound. Vibr. 137, 369-384) is presented. Based on a recursive rather than a successive approximation formula, the present refined formulation always makes use of a 6 x 6 frequency determinant, regardless of the number of layers of the laminated shell or panel considered. Upon comparing its results with corresponding numerical results available in the literature, the effectiveness of the approach in producing the exact frequencies of vibration is checked. Moreover, further detailed numerical results dealing with flexural vibration frequencies and corresponding mode shapes of laminated cylinders and cylindrical panels having symmetric or regular antisymmetric cross-ply lay-up are presented, studied and discussed.

Three-dimensional stress analysis of orthotropic and cross-ply laminated hollow cylinders and cylindrical panels

This paper deals with a detailed, three-dimensional stress and displacement analysis of transversely loaded, laminated complete hollow cylinders and open cylindrical panels having a symmetric or an antisymmetric cross-ply lay-up. The analysis is based on a refined, static version of a successive approximation approach which was first proposed by Soldatos and Hadjigeorgiou (J. Sound Vibration 137 (1990) 369-384) in connection with corresponding dynamic problems. However, the present refined formulation makes use of a recursive rather than a successive approximation formula. As a result, independently of the number of layers employed, the solution of the bending problem considered always ends with the solution of a sixth order system of simultaneous algebraic equations. The effectiveness of the approach employed is checked by comparing numerical results with corresponding three-dimensional elasticity results published elsewhere in the literature. Then, the proposed formulation is further used towards a detailed stress and displacement analysis of the afore-mentioned structural elements.

A state space finite element for laminated composite plates

This paper presents a semi-analytical finite element solution for the stress analysis of cross-ply laminated composite plates. The method is based on a mixed variational principle that includes the variations of both displacements and stresses. Finite element approximation is introduced only for the in-plane variations of displacements and stresses, while the through-thickness distributions of them are obtained by using the method of state equation. Numerical tests show that the results obtained approach the analytical three-dimensional solutions. Moreover, the use of the recursive formulation of the state equation leads to the solution of an algebra equation system whose order does not depend on the number of material layers of the laminate. Compared with the traditional finite element method, the new solution always provides continuous distributions of both displacements and transverse stresses across material interfaces.

Three-dimensional buckling analysis of laminated composite hollow cylinders and cylindrical panels

Abstract The buckling problem of thick, cross-ply laminated cylinders and cylindrical panels under combined external loading is investigated on the basis of fully three-dimensional elasticity considerations. The three-dimensional pre-buckling state that is initially employed, assumes zero shear stresses and is suitable for the analysis of both open panels and closed cylinders. This assumption leads to a set of three-dimensional linearized buckling equations. Both sets of three-dimensional prebuckling and buckling equations are then solved on the basis of a recursive method. The analysis is suitable for studying the buckling behavior of simply supported cross-ply cylinders, subjected to the single or the combined action of an axial compression and a uniform lateral pressure, or open cross-ply cylindrical panels under axial compression. The numerical results presented and discussed throughout this paper deal with cylinders and cylindrical panels having a symmetric or an antisymmetric cross-ply lay-up.

A three-dimensional free vibration analysis of cross-ply laminated rectangular plates with clamped edges

On the basis of three-dimensional elasticity, this paper presents a free vibration analysis of cross-ply laminated rectangular plates with clamped boundaries. The analysis is based on a recursive solution suitable for three-dimensional vibration analysis of simply supported plates. Clamped boundary conditions are imposed by suppressing the edge displacements of a number of planes which are parallel to the mid-plane. This is achieved by coupling a number of different vibration modes of the corresponding simply supported plate using a Lagrange multiplier method. A satisfactory solution can be obtained by choosing suitably larger numbers of the coupled vibration modes and the fixed planes across the thickness of the plate. Numerical results are presented to show the convergence of the solution. Results are also obtained for either isotropic or cross-ply laminated plates having different combinations of simply supported and clamped boundaries.

Microscopic modelling of the hydraulic fracturing process

A microscopic perspective is introduced in this study which offers a detailed insight at the inter-particle level to the geo-mechanical responses caused by fluid injection and the resulting pressure build-up. This was achieved by employing the Discrete Element Method (DEM) to model the pressure development and the subsequent fracturing and/or cavity propagation. This technique represents the formation material as an assembly of discrete particles linked to each other through contacts. Numerical experiments were carried out on two sample materials. For the first instance, tests were carried out on a bulk material, representative of a generic intact rock, with the breakage of inter-particle bonds indicating the formation of cracks. The second series of tests was carried out on granular type materials such as sand, where particle separation signified cavity initiation and separation. It was observed from the DEM modelling results that the intact rock material showed a predominance of mode II fracturing at high fluid velocities. However, when the fluid velocity is reduced considerably the fracturing behaviour tended towards more of mode I. Also, records of the pressure development were taken from the numerical results and were used to monitor the fracturing events. The outcome of this study highlights important aspects of the hydraulic fracturing process especially at the particle–particle scale, and thus provides a strong basis for more exhaustive studies involving larger scale reservoir modelling and more complex fracturing scenarios.

INTERFACIAL SHEAR TRANSFER OF RC BEAMS STRENGTHENED BY BONDED COMPOSITE PLATES

Abstract In this paper an analytical method is proposed to predict the distributions of interfacial shear stress in concrete beams strengthened by composite plates. Non-linear behaviour of concrete under compression is considered in the analysis. The solutions show significant shear stress concentration near the cut-off end of plates. A parametrical study is carried out to show the effects of some design variables, e.g., thickness of adhesive layer, material properties and the distance from support to cut-off end of bonded plates.

3D analysis of stress transfer in the micromechanics of fiber reinforced composites by using an eigen-function expansion method

This paper presents an exact solution for an inhomogeneous, transversely isotropic, elastic circular cylinder subjected to axisymmetric force and displacement boundary conditions. The solution is obtained on the basis of an eigen-function expansion method and can satisfy all the boundary conditions prescribed on the curved and end surfaces of the cylinder. It can be used directly in the micromechanical analysis of fiber reinforced composites to investigate the typical Representative Volume Element (RVE). The element consists of a combined circular cylinder composed of a solid inner circular cylinder of transversely isotropic fiber and a concentric outer circular cylinder of isotropic matrix material. Using this solution, all the stress and displacement components of both the inner fiber and the outer matrix, and hence the stress transfer in the interface between the fiber and matrix, are expressed analytically. The numerical results presented show that stress concentration occurs near the ends of the cylinder where external forces are applied.

Three-dimensional vibration of laminated composite plates and cylindrical panels with arbitrarily located lateral surfaces point supports

On the basis of fully three-dimensional elasticity considerations, this paper presents a free vibration analysis of simply supported, cross-ply laminated plates and cylindrical panels that are subjected to an arbitrary number of lateral surfaces point supports. The analysis is based on a recursive approach suitable for the vibration analysis of corresponding unconstrained structural elements. By means of dynamic equilibrium considerations, the reaction of the point supports is imposed by using the Lagrange multipliers method. This yields the eigendeterminant of a constrained panel by appropriately coupling the response of a suitably large number of natural vibration modes of the corresponding unconstrained structural element.

Wave propagation in anisotropic laminated hollow cylinders of infinite extent

This paper deals with a three‐dimensional elasticity investigation of wave propagation in an infinitely long hollow cylinder whose homogeneous or layered structure is made by generally orthotropic or monoclinic materials. The analysis is based on a recursive formulation of a successive approximation method employed elsewhere by the authors for the study of axisymmetric and flexural vibrations of homogeneous orthotropic and cross‐ply laminated hollow cylinders of finite length. The method has further been applied in connection with static and thermoelastic analyses of orthotropic homogeneous and cross‐ply laminated cylinders and cylindrical panels. In all cases considered, results of this approach converge very rapidly toward corresponding exact three‐dimensional elasticity results. Hence the present study is based on essentially exact three‐dimensional elasticity results and is further expected to serve as a benchmark for corresponding future investigations based on finite element and/or two‐dimensional shell theory formulations.