高层框筒结构正交各向异性等效模型的解析解

基于正交各向异性连续化等效模型，将高层框筒结构转换成弹性力学平面应力平板组合结构，并采用应力函数法获得了解析解．

正交各向异性材料中微裂纹的最大屏蔽效应

通过对正交各向异性材料中不同的微裂纹屏蔽源泉的分析，发现在Ｈｕｔｃｈｉｎｓｏｎ所指出的屏蔽效应的第２个源泉（即微裂纹形成引起的残余应力释放导致应力场的再分布）中，还应计及微裂纹形成引起的远场应力在微裂纹处产生的应力场的释放（可称为诱导应力），从而应重新考虑应力场的分布，在文中所研究的各向异性脆性材料中，在计及诱导应力释放对应力场的影响及局部材料刚度下降的影响时，当微裂纹倾角与微裂纹处的最大拉应力方向垂直时，微裂纹对主裂纹的屏蔽效应达到最大值，该结果与Ｏｒｔｉｚ在连续损伤力学的构架下得到的结果一致．

Green函数法计算弹性地基钢筋混凝土板

将钢筋混凝土板在特定域中的Green函数作为影响函数 ,首先根据板的外边界条件以及非均匀弹性地基条件建立方程 ,求出虚拟域中的Green函数“源” ,继而由求得的“源值”和板上的已知荷载确定板内任意点的挠度和内力。该方法简单实用 ,易于编程 ,适用于任意形状 ,多种边界条件以及非均匀弹性地基的钢筋混凝土弹性薄板。文中附有算例 ,并将其数值结果与解析解比较 ,表明该方法精度良好。

Seismic AVAZ inversion for orthorhombic shale reservoirs in the Longmaxi area, Sichuan

Seismic AVAZ inversion method based on an orthorhombic model can be used to invert anisotropy parameters of the Longmaxi shale gas reservoir in the Sichuan Basin..As traditional seismic inversion workfl ow does not suffi ciently consider the infl uence of fracture orientation,we predict fracture orientation using the method based on the Fourier series to correct pre-stacked azimuth gathers to guarantee the accuracy of input data,and then conduct seismic AVAZ inversion based on the VTI constraints and Bayesian framework to predict anisotropy parameters of the shale gas reservoir in the study area.We further analyze the rock physical relation between anisotropy parameters and fracture compliance and mineral content for quantitative interpretation of seismic inversion results.Research results reveal that the inverted anisotropy parameters are related to P-and S-wave respectively,and thus can be used to distinguish the effect of fracture and fl uids by the joint interpretation.Meanwhile high values of anisotropy parameters correspond to high values of fracture compliance,so the anisotropy parameters can refl ect the development of fractures in reservoir.There is two sets of data from different sources,including the content of brittle mineral quartz obtained from well data and the anisotropy parameters inverted from seismic data,also show the positive correlation.This further indicates high content of brittle mineral makes fractures developing in shale reservoir and enhances seismic anisotropy of the shale reservoir.The inversion results demonstrate the characterization of fractures and brittleness for the Longmaxi shale gas reservoir in the Sichuan Basin.

Stepwise inversion method for determining anisotropy parameters in a horizontal transversely isotropic formation

The anisotropy of a geologic formation can reflect the direction of fractures and ground stress, which is an important metric that guides the exploration and development of oil and gas reservoirs. Cross-dipole acoustic logging is the main method used to detect anisotropy with borehole geophysics. In this paper, a stepwise inversion method for three anisotropy parameters in a horizontal transversely isotropic(HTI) formation is proposed, which turns one 3D operation of simultaneous inversion into three 1D operations. The scheme’s stability and reliability were tested by numerically simulated data using a f inite-difference method, and by f ield logging data. The inversion results of the simulated data show that the stepwise inversion method can stably obtain the fast shear azimuth and the anisotropy parameters in both fast and slow formations with strong and weak anisotropy, and it performed well even with noisy data. In particular, the results of the fast shear azimuth inversion were very stable and reliable. The inversion results of f ield logging data were consistent with those given by existing commercial software, which used simultaneous inversion, for both fast and slow formations. Where large difference was observed between our stepwise method and the commercial software, our analysis suggests that the fast shear azimuth of our inversion was more reasonable, which reinforces its superior performance and practicality.

General solutions for special orthotropic piezoelectric media

This paper presents the forms of the general solution for general anisotropic piezoelectric media starting from the basic equations of piezoelasticity by using the operator method introduced by Lur’e (1964), and gives the analytical form of the general solution for special orthotropic piezoelectric media. This paper uses the non-uniqueness of the general solution to obtain the generalized LHN solution and the generalized E-L solution for special orthotropic piezoelectric media. When the special orthotropic piezoelectric media degenerate to transversely piezoelectric media, the solution given by this paper degenerates to the solution for transversely isotropic piezoelectric media accordingly, so that this paper generalized the results in transversely isotropic piezoelectric media.

Determination of Key Cohesive Zone Model’s Parameters for Orthotropic Paper and Its Static Fracture Simulation

Investigation of paper cutting process is vital for the design of cutting tools,but the fracture mechanism of paper cutting is still unclear.Here,we focus on the cutting process of paper,including the key parameters of cohesive zone model(CZM)for the orthotropic paper,to simulate the shear fracture process.Firstly,the material constants of the orthotropic paper are determined by longitudinal and transverse tensile test.Secondly,based on the tensile stressstrain curves,combined with damage theory and numerical simulations,the key parameters of the CZM for the orthotropic paper are obtained.Finally,a model III fracture is simulated to verify the accuracy of the model.Results show that the load-displacement curves obtained by the simulation is consistent with the test results.

A state space solution for the bending problem of thick laminated piezoelectric open cylindrical shells

Based on the theories of three-dimensional elasticity and piezoelectricity, and by assuming appropriate boundary functions, we established a state equation of piezoelectric cylindrical shells. By using the transfer matrix method, we presented an analytical solution that satisfies all the arbitrary boundary conditions at boundary edges, as well as on upper and bottom surfaces. Our solution takes into account all the independent elastic and piezoelectric constants for a piezoelectric orthotropy, and satisfies continuity conditions between plies of the laminates. The principle of the present method and corresponding results can be widely used in many engineering fields and be applied to assess the effectiveness of various approximate and numerical models.

Analytical Solutions to the Fundamental Frequency of Arbitrary Laminated Plates under Various Boundary Conditions

In recent years, as the composite laminated plates are widely used in engineering practice such as aerospace, marine and building engineering, the vibration problem of the composite laminated plates is becoming more and more important. Frequency, especially the fundamental frequency, has been considered as an important factor in vibration problem. In this paper, a calculation method of the fundamental frequency of arbitrary laminated plates under various boundary conditions is proposed. The vibration differential equation of the laminated plates is established at the beginning of this paper and the frequency formulae of specialty orthotropic laminated plates under various boundary conditions and antisymmetric angle-ply laminated plates with simply-supported edges are investigated. They are proved to be correct. Simple algorithm of the fundamental frequency for multilayer antisymmetric and arbitrary laminated plates under various boundary conditions is studied by a series of typical examples. From the perspective of coupling, when the number of laminated plates layers N〉8-10, some coupling influence on the fundamental frequency can be neglected. It is reasonable to use specialty orthotropic laminated plates with the same thickness but less layers to calculate the corresponding fundamental frequency of laminated plates. Several examples are conducted to prove correctness of this conclusion. At the end of this paper, the influence of the selected number of layers of specialty orthotropic laminates on the fundamental frequency is investigated. The accuracy and complexity are determined by the number of layers. It is necessary to use proper number of layers of special orthotropic laminates with the same thickness to simulate the fundamental frequency in different boundary conditions.

Analytical Approaches of Composite Rectangular Thin Plates

The purpose of the present study was to explore and subsequently establish a technique for determination of analytical solutions for the differential equation for composite thin plates. The considered reasons for the solutions were to exactly satisfy the boundary conditions and to verify as close as possible the differential equation of the plate. There are studied two solutions for orthotropic plate with clamped edges, and made comparisons with the solutions presented by Reddy [1] and with the exact solution by Timoshenko and Woinowsky. The models are based on the CLPT （classical laminated plate theory）. The Ritz method, in conjunction with the weighted residue method for the coefficients calculation, is used to analytically determine the bending solutions of orthotropic laminated plates subjected to uniform pressure on the bottom laminate. The purposed solutions were critically analysed considering a FEM （finite element method） solution for comparison. Finally, it is presented the experimental device and the experimental test results, as well. Fabrics have been incorporated into two composite plates were required scalps on one direction, thus ensuring different elasticity modules on both directions. Thorough comparison between analytical solutions, numerical results and experimental data is performed and a good agreement is obtained.

Analytical Solution for Thermo-Electro-Elastic Problems of an Orthotropic Piezoelectric Hollow Cylinder Subjected to Various Loading

An interpolation method was used to solve the Volterra integral equation of the second kind caused by interaction among thermal, electric and mechanical fields. The exact expressions for the transient responses of stresses, electric displacement and electric potential in an orthotropic piezoelectric hollow cylinder were obtained by means of the finite integral transforms. From the sample numerical calculations, it is seen that the present method is suitable for an orthotropic piezoelectric hollow cylinder subjected to arbitrary thermal shock, mechanical load and transient electric excitation. The result can be used as a reference to solve other transient coupled problems of thermo-electro-elasticity.

Study of Torsional Impact Problem of Orthotropic Hollow Cylinder

A simple integral transform method was presented to solve the torsional impact problem of orthotropic hollow cylinder with mixed boundary condition. The analytical solution for the torsional impact problem of the orthotropic hollow cylinder was got. Some examples were calculated and discussed.

The edge crack problem for an orthotropic functionally graded strip under concentrated loads

The plane crack problem of an orthotropic functionally graded strip under concentrated loads is studied. The edge crack is perpendicular to the boundary and the elastic property of the material is assumed to vary depending on thickness. By using an integral transform method, the present problem can be reduced to a single integral equation which is solved numerically. The influences of parameters such as the nonhomogeneity constant and the geometry parameters on the stress intensity factors (SIFs) are studied. It is found that the nonhomogeneity constant has important influences on the SIFs.

Finite element formulation of axisymmetric heat transfer problem for orthotropic materials

By using Galerkin’s method, the finite element formulation is made for axisymmtric heat transfer problems for anisotropic materials from the heat transfer differential equations expressed in terms of heat fluid density. Results of an example show that the heat transfer anisotropy has an important effect on temperature field.

Mathematical Model of Dynamics of Micropolar Orthotropic Elastic Thin Bars with Free Fields of Displacements and Rotations

In the present paper, initial-boundary value problem of plane stress state of micropolar theory of elasticity is considered for orthotropic material in the domain of thin rectangle. General hypotheses are formulated, which are the qualitative results of the asymptotic method of integration of the stated initial-boundary value problem. On the basis of the accepted hypotheses general applied one-dimensional models of dynamics of bending deformation of micropolar orthotropic elastic thin bars with free fields of displacements and rotations are constructed with and without consideration of shear deformations. With the help of the constructed models different dynamic problems of micropolar bars can be studied. Here concrete problems of free and forced vibrations of hinged supported micropolar orthotropic elastic thin bar are studied. Numerical analysis is done and specific features of dynamic characteristics of micropolar material are revealed. Particularly, it is shown that there is a frequency of vibrations of the micropolar bar that does not depend on bar sizes.

Stress Analysis of a Circularly-Perforated Finite Orthotropic Composite Plate

Stresses, particularly those at geometric discontinuities, can influence structural integrity of engineering components. Motivated by the prevalence of cutouts in components, the objective of this paper is to demonstrate ability to stress analyze finite, circularly-perforated orthotropic composites whose external loading may be unknown. Recognizing difficulties in obtaining purely theoretical or numerical solutions, the paper presents a hybrid means of stress analyzing such structures. Individual stresses, including those on the edge of the hole, are obtained in a loaded finite graphite/epoxy composite tensile plate containing a round hole by processing measured values of a single displacement field with an Airy stress function in complex variables. Displacements are recorded by digital image correlation. Traction-free conditions are satisfied analytically at the edge of the hole using conformal mapping and analytic continuation. Stresses satisfy equilibrium and strains satisfy compatibility. Significant features of the technique include its wide applicability, it smooths the measured information, does not require knowing the applied loading, and the rigorous mechanics foundation by which strains are determined from measured displacements.

Analysis of Critical Load of the Orthotropic Plate Structures

Advanced design based on the concept of orthotropic structure includes better use of materials, less weight compared to the equivalent isotropic construction and controlled effectively reserve resistance in all its segments. In this case a calculation of critical load is exposed using the FDM （Finite Difference Method） concept of thin plates subjected to complex loads due to forces in the middle-plane. Results of calculation model, discussed in this paper, are given in graphic form. Presented results should serve as an indicator of the expansion of theoretical base of similar models, which can be reasonably use by researchers and engineers in their practices, and by students for educational purposes.

A Quadrature Approach for N-Collinear Crack Problem in an Orthotropic Strip

This study presents the determination of the stress intensity factors （SIFs） at the edges of the cracks in an elastic strip weakened by N-collinear cracks. The problem of an orthotropic elastic strip is reduced to a system of Cauchy type singular integral equations. The system of singular integral equations is approached by a Quadrature technique. Under two different loading conditions, the results are obtained for the different cases of crack numbers. The resistance of the strip is examined by considering the orthotropic properties of the strip material. Finally, the crack interactions are clarified during the analysis.

Welding Problem of Two Different OrthotropicElastic Strips

In this paper,welding problem of two orthotropic elastic strips with dissimilarmaterials is studied. By means of plane elastic complex method and theory of integralequation, a new algorithm is given, which improves the usual method of purely integraltransformation.Theoretically, the stress distribution is obtained in a closed form.

Generalization of Hill's yield criterion to tension-compression asymmetry materials

This paper is devoted to developing a yield criterion that can model the asymmetry and anisotropy in yielding of pressure insensitive metals,in terms of accuracy and simplicity of formulation.First,a new isotropic yield criterion,which can model the asymmetry in yielding of pressure insensitive metals,is proposed.Further,using Cazacu's generalizations to anisotropic conditions of the invariants of the deviatoric stress,the proposed isotropic yield criterion is extended to orthotropy.The proposed anisotropic criterion has a quite simple form,and the number of material constants involved is only half of that of Cazacu's(2004) yield criterion.Compared to Hill's(1948) yield criterion,the proposed anisotropic yield criterion has three additional constants,which are used to model the tension-compression asymmetry of materials.All the material constants involved in the criterion can be determined by simple tests.The proposed criterion reduces to Hill's(1948) yield criterion if the tensile and compressive yield stresses are equal.In other words,the proposed anisotropic yield criterion can be considered as an extension of Hill's(1948) criterion to tension-compression asymmetry materials.The anisotropic yield criterion is used to describe the plastic response of Cu-Al-Be shape memory alloy(data after Laydi and Lexcellent) and Ni3Al based intermetallic alloy IC10 sheets.It is shown that the proposed yield criterion can describe very well the asymmetry and anisotropy observed in those materials.