Band gaps of 2D phononic crystal with orthotropic cylindrical fillers embedded in the isotropic host are studied in this paper. Two kinds of periodic structures, namely, the square lattice and the triangle lattice, ar...Band gaps of 2D phononic crystal with orthotropic cylindrical fillers embedded in the isotropic host are studied in this paper. Two kinds of periodic structures, namely, the square lattice and the triangle lattice, are considered. For anisotropic phononic crystal, band gaps not only depend on the periodic lattice but also the angle between the symmetry axis of orthotropic material and that of the periodic structure. Rotating these cylindrical fillers makes the angle changing continuously; as a result, pass bands and forbidden bands of the phononic crystal are changed. The plane wave expansion method is used to reduce the band gap problem to an eigenvalue problem. The numerical example is given for YBCO/Epoxy composites. The location and the width of band gaps are estimated for different rotating angles. The influence of anisotropy on band gaps is discussed based on numerical results.展开更多
A set of nonlinearly coupled algebraic and differential eigenvalue equations of nonlinear axisymmetric free vibration of orthotropic shallow thin spherical and conical shells are formulated following an assumed time-m...A set of nonlinearly coupled algebraic and differential eigenvalue equations of nonlinear axisymmetric free vibration of orthotropic shallow thin spherical and conical shells are formulated following an assumed time-mode approach suggested in this paper. Analytic solutions are presented and an asymptotic relation for the amplitude-frequency response of the shells is derived. The effects of geometrical and material parameters on vibrations of the shells are investigated.展开更多
A rotating ellipsoid composed of an orthotropic piezoelectricmaterial (2mm) are considered, and the stress and electricdisplacement fields in this rotating ellipsoid are obtained exactlyand completely. The solutions o...A rotating ellipsoid composed of an orthotropic piezoelectricmaterial (2mm) are considered, and the stress and electricdisplacement fields in this rotating ellipsoid are obtained exactlyand completely. The solutions of the same problem for transverselyisotropic piezoelectric material (6 mm) are also given byDegenerating above results. At last, numerical examples for fourkinds of media are illustrated in figures for Comparison.展开更多
Discarding any assumption about displacement models and stress distribution andintroducing δ-function into the present study, we established the state equation for thecontinuous orthotropic open cylindrical shells. A...Discarding any assumption about displacement models and stress distribution andintroducing δ-function into the present study, we established the state equation for thecontinuous orthotropic open cylindrical shells. An thentical exocl solution is presentedfor the statics of thin. moderately thick and thick laminated continuous openrylindrical shells. Numerical results are obtained and compared with those calculatedusing SAP5.展开更多
In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed...In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed. The analytical solution for the relationship between forcing frequency and amplitude of vibration is obtained by Galerkin's method. Finally, the paper analyses the effect of the transverse shear on the vibration of the plate and gives the ratio of nonlinear period to linear period for nonlinear free vibration of the plate.展开更多
A new Don-quadratic orthotropic yield function is developed in the present paper.It does not have those limitatioins which existing non-quadratic anisotropic yield functions have,such as being usable only for the plan...A new Don-quadratic orthotropic yield function is developed in the present paper.It does not have those limitatioins which existing non-quadratic anisotropic yield functions have,such as being usable only for the plane stress problems and in-plane isotropic sheet metals,and that the directions of principal stress or the ex ponent in yield function can not be arbitrary,etc.Furthermore all of the material constants involved in this yield function can be determined by performing only uniaxial tension lest.This yield function contains three new parameters,of which each one is present for one principal plane of anisotropy.Their values can be.generally,selected to equal 3.Other methods to determine the value of these parmeters are discussed and given in this paper.From the regression estimate for the yield stress in five directions of several kinds of titanium metal sheet.it is obtained that the suitable value of exponent in yield function for titanium sheets is 6 or 8.This is confirmed from the use for several plastic deformation problems of titanium sheets.展开更多
Discarding any ussumption regarding displacement or strers models, the stateequation for orthotropy is established in a cylindrical system. The exact solution ispresented for the statics of thick closed laminated cant...Discarding any ussumption regarding displacement or strers models, the stateequation for orthotropy is established in a cylindrical system. The exact solution ispresented for the statics of thick closed laminated cantilever cylindrical shells. Everyequation of elasticity can be satisfied and all the elastic constants are taken intoaccount. Arbitrary precision of a desired order can be obtained.展开更多
The effect of Pasternak foundation and non-homogenity on the axisymmetric vibrations of polar orthotropic parabolically varying tapered circular plates has been analyzed on the basis of classical plate theory. Ritz me...The effect of Pasternak foundation and non-homogenity on the axisymmetric vibrations of polar orthotropic parabolically varying tapered circular plates has been analyzed on the basis of classical plate theory. Ritz method has been used to find the numerical solution of the specified problem. The efficiency of the Ritz method depends on the choice of basis function based upon deflection of polar orthotropic plates. The effects of different plate parameters viz. elastic foundation, non-homogeneity, taper parameter and that of orthotropy on fundamental, second and third mode of vibration have been studied for clamped and simply-supported boundary conditions. Mode shapes for specified plates have been drawn for both the boundary conditions. Convergence and comparison studies have been carried out for specified plates.展开更多
A technique for solving the three-dimensional problem of bending in the theory of elasticity in orthotropic plates of variable thickness is developed in the paper. On the basis of the method of expansion of displaceme...A technique for solving the three-dimensional problem of bending in the theory of elasticity in orthotropic plates of variable thickness is developed in the paper. On the basis of the method of expansion of displacements into an infinite series, the problem has been reduced to the solutions of two independent problems, which are described by two independent systems of two-dimensional infinite equations.展开更多
This paper is devoted to the development of new theory of orthotropic thick plates with account of internal forces, moments and bimoments. An equation of motion of plates is described by two systems with nine equation...This paper is devoted to the development of new theory of orthotropic thick plates with account of internal forces, moments and bimoments. An equation of motion of plates is described by two systems with nine equations each. Boundary conditions depended on displacements, forces, moments and bimoments are given. An exact solution of the bending of thick plate under the effect of sine load is built. Numerical results for maximal values of displacements and stresses of the plate are obtained.展开更多
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 demonstr...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.展开更多
Without any assumptions about displacement models and stress distribution, the state equation for orthotropy is established in a cylindrical coordinate system. The exact solutions are presented for the statics, dynami...Without any assumptions about displacement models and stress distribution, the state equation for orthotropy is established in a cylindrical coordinate system. The exact solutions are presented for the statics, dynamics and buckling of thick open laminated cylindrical shells by means of the Cayley-Hamilton theorem. No matter how many layers are considered, the calculation always leads to solving a set of linear algebraic equations of three unknowns. Every equation of elasticity can be satisfied and all the elastic constants can be taken into account. Precision of the desired order can be obtained.展开更多
基金supported by the National Natural Science Foundation of China (No.10672019)
文摘Band gaps of 2D phononic crystal with orthotropic cylindrical fillers embedded in the isotropic host are studied in this paper. Two kinds of periodic structures, namely, the square lattice and the triangle lattice, are considered. For anisotropic phononic crystal, band gaps not only depend on the periodic lattice but also the angle between the symmetry axis of orthotropic material and that of the periodic structure. Rotating these cylindrical fillers makes the angle changing continuously; as a result, pass bands and forbidden bands of the phononic crystal are changed. The plane wave expansion method is used to reduce the band gap problem to an eigenvalue problem. The numerical example is given for YBCO/Epoxy composites. The location and the width of band gaps are estimated for different rotating angles. The influence of anisotropy on band gaps is discussed based on numerical results.
基金Project supported by the National Natural Science Foundation of China
文摘A set of nonlinearly coupled algebraic and differential eigenvalue equations of nonlinear axisymmetric free vibration of orthotropic shallow thin spherical and conical shells are formulated following an assumed time-mode approach suggested in this paper. Analytic solutions are presented and an asymptotic relation for the amplitude-frequency response of the shells is derived. The effects of geometrical and material parameters on vibrations of the shells are investigated.
基金the National Natural Science Foundation of China (No.19872060).
文摘A rotating ellipsoid composed of an orthotropic piezoelectricmaterial (2mm) are considered, and the stress and electricdisplacement fields in this rotating ellipsoid are obtained exactlyand completely. The solutions of the same problem for transverselyisotropic piezoelectric material (6 mm) are also given byDegenerating above results. At last, numerical examples for fourkinds of media are illustrated in figures for Comparison.
文摘Discarding any assumption about displacement models and stress distribution andintroducing δ-function into the present study, we established the state equation for thecontinuous orthotropic open cylindrical shells. An thentical exocl solution is presentedfor the statics of thin. moderately thick and thick laminated continuous openrylindrical shells. Numerical results are obtained and compared with those calculatedusing SAP5.
文摘In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed. The analytical solution for the relationship between forcing frequency and amplitude of vibration is obtained by Galerkin's method. Finally, the paper analyses the effect of the transverse shear on the vibration of the plate and gives the ratio of nonlinear period to linear period for nonlinear free vibration of the plate.
基金supported by Science Foundation of Aeronautics of China
文摘A new Don-quadratic orthotropic yield function is developed in the present paper.It does not have those limitatioins which existing non-quadratic anisotropic yield functions have,such as being usable only for the plane stress problems and in-plane isotropic sheet metals,and that the directions of principal stress or the ex ponent in yield function can not be arbitrary,etc.Furthermore all of the material constants involved in this yield function can be determined by performing only uniaxial tension lest.This yield function contains three new parameters,of which each one is present for one principal plane of anisotropy.Their values can be.generally,selected to equal 3.Other methods to determine the value of these parmeters are discussed and given in this paper.From the regression estimate for the yield stress in five directions of several kinds of titanium metal sheet.it is obtained that the suitable value of exponent in yield function for titanium sheets is 6 or 8.This is confirmed from the use for several plastic deformation problems of titanium sheets.
文摘Discarding any ussumption regarding displacement or strers models, the stateequation for orthotropy is established in a cylindrical system. The exact solution ispresented for the statics of thick closed laminated cantilever cylindrical shells. Everyequation of elasticity can be satisfied and all the elastic constants are taken intoaccount. Arbitrary precision of a desired order can be obtained.
文摘The effect of Pasternak foundation and non-homogenity on the axisymmetric vibrations of polar orthotropic parabolically varying tapered circular plates has been analyzed on the basis of classical plate theory. Ritz method has been used to find the numerical solution of the specified problem. The efficiency of the Ritz method depends on the choice of basis function based upon deflection of polar orthotropic plates. The effects of different plate parameters viz. elastic foundation, non-homogeneity, taper parameter and that of orthotropy on fundamental, second and third mode of vibration have been studied for clamped and simply-supported boundary conditions. Mode shapes for specified plates have been drawn for both the boundary conditions. Convergence and comparison studies have been carried out for specified plates.
文摘A technique for solving the three-dimensional problem of bending in the theory of elasticity in orthotropic plates of variable thickness is developed in the paper. On the basis of the method of expansion of displacements into an infinite series, the problem has been reduced to the solutions of two independent problems, which are described by two independent systems of two-dimensional infinite equations.
文摘This paper is devoted to the development of new theory of orthotropic thick plates with account of internal forces, moments and bimoments. An equation of motion of plates is described by two systems with nine equations each. Boundary conditions depended on displacements, forces, moments and bimoments are given. An exact solution of the bending of thick plate under the effect of sine load is built. Numerical results for maximal values of displacements and stresses of the plate are obtained.
文摘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.
基金Project supported by the National Natural Science Foundation of China
文摘Without any assumptions about displacement models and stress distribution, the state equation for orthotropy is established in a cylindrical coordinate system. The exact solutions are presented for the statics, dynamics and buckling of thick open laminated cylindrical shells by means of the Cayley-Hamilton theorem. No matter how many layers are considered, the calculation always leads to solving a set of linear algebraic equations of three unknowns. Every equation of elasticity can be satisfied and all the elastic constants can be taken into account. Precision of the desired order can be obtained.
