Elastoplastic stress-strain state of flexible layered shells made of isotropic and transversely isotropic materials with different moduli and subjected to axisymmetric loading

The paper proposes a numerical technique for analysis of the elastoplastic stress-strain state of flexible layered shells of revolution under axisymmetric loading. It is assumed that the shells are made of isotropic and transversely isotropic materials with different moduli in tension and compression. The technique is based on a geometrically nonlinear theory of shells that takes into account the squared angles of rotation and the Kirchhoff-Love hypotheses for a layer stack. The deformation of isotropic materials is described using the theory of deformation along paths of small curvature. The deformation of transversely isotropic materials is described using the theory of elasticity with different moduli in tension and compression. The problem is solved by the method of successive approximations. A numerical example is given __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 31–42, November 2007.     

Axisymmetric thermoelastoplastic stress-strain state of transversely isotropic laminated shells

The method of successive approximations is used to determine the thermoelastoplastic stress-strain state of isotropic and transversally isotropic laminated shells of revolution under axisymmetric loading. Hill’s theory of plasticity with isotropic hardening is used to describe the deformation of transversely isotropic materials, while the theory of deformation along paths of small curvature is used to describe the deformation of isotropic materials. The elastoplastic stress-strain state of a two-layer cylindrical shell under mechanical and thermal loads is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 71–80, June 2006.     

Thermoelastoplastic Stress—Strain State of Laminated Transversely Isotropic Shells under Axisymmetric Loading

A method is proposed for determining the thermoelastoplastic stress–strain state of laminated shells of revolution, made of isotropic and transversely isotropic materials, under axisymmetric loading. The method is based on the Kirchhoff–Love hypotheses for a layer stack, the theory of deformation along paths of small curvature for isotropic materials, and Hill's flow theory with isotropic hardening for transversely isotropic materials. The loading history is accounted for. The problem is solved by the method of successive approximations. Numerical examples are given     

Elastoplastic Axisymmetric Stress-Strain State of Laminated Shells Made of Isotropic and Transversely Isotropic Materials with Different Moduli

A method is developed for analysis of the elastoplastic stress-strain state of laminated shells of revolution under axisymmetric loading. The shells are made of isotropic and transversally isotropic materials with different moduli. The method is based on the Kirchhoff-Love hypotheses for the whole laminate, the theory of deformation along paths of small curvature (for isotropic materials), and the theory of elasticity with different tensile and compressive moduli (transversely isotropic materials). The problem is solved by the method of successive approximations. Numerical examples are given __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 88–96, August 2005.     

The nonaxisymmetric thermostressed state of laminated isotropic and rectilinearly orthotropic solids of revolution

A technique for determination of the nonaxisymmetric elastoplastic stress-strain state of laminated isotropic and rectilinearly orthotropic solids of revolution under nonisothermal loading is described. The semianalytic method of finite elements is used together with the method of successive approximations. The deformation of isotropic materials is described by the equations of the theory of deformation along trajectories of small curvature, and the deformation of orthotropic materials is described by the equations of the theory of elasticity. The thermostressed state of a three-layered solid of revolution of complex form made from isotropic and cylindrically and rectilinearly orthotropic materials subject to nonaxisymmetric heating is studied. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 4, pp. 88–95, April, 2000.     

Thermoelastoplastic axisymmetric stress-strain state of laminated orthotropic shells

A method is proposed for the numerical analysis of the thermoelastoplastic stress-strain state of laminated shells of revolution, made of isotropic and orthotropic materials, under axisymmetric loading. The method is based on the Kirchhoff-Love hypotheses for a layer stack, the theory of deformation along paths of small curvature for isotropic materials, and Hills theory of flow with isotropic hardening for orthotropic materials. The problem is solved by the method of successive approximations. A numerical example is given.__________Translated from Prikladnaya Mekhanika, Vol. 40, No. 12, pp. 84–91, December 2004.     

The Thermoviscoelastoplastic Axisymmetric Stress–Strain State of Laminated Flexible Orthotropic Shells

A technique is proposed to determine the thermoviscoelastoplastic axisymmetric stress–strain state of laminated shells made of isotropic and orthotropic materials. The paper deals with processes of shell loading such that both instantaneous elastoplastic and creep strains occur in isotropic materials and elastic and creep strains in orthotropic materials. The technique is developed within the framework of the Kirchhoff–Love hypotheses for a stack of layers with the use of the equations of the geometrically nonlinear theory of shells in a quadratic approximation. The deformation of isotropic materials is described by the equations of the theory of deformation along slightly curved trajectories, while the deformation of orthotropic materials is described by Hooke's law with additional terms allowing for creep. A numerical example is given     

Deformation and Microdamage of a Discrete-Fibrous Composite with Transversely Isotropic Components

The theory of microdamage for materials with a transversely isotropic matrix and unidirectional ellipsoid-like fibers is set forth. Microdamage is modeled by empty pores. The failure criterion for a microvolume is assumed to have the Huber–Mises form where the ultimate strength is a random function of coordinates with a power or Weibull distribution. The stress–strain state and effective properties of the material are determined from the theory of elasticity for materials with a transversely isotropic matrix and unidirectional fibers. The deformation and microdamage equations are closed by the porosity-balance equations. The nonlinear dependences of the coupled processes of deformation and microdamage on macrodeformations are constructed. The effect of physical and geometrical parameters on the processes is studied     

The nonaxisymmetric elastoplastic state of isotropic and cylindrically orthotropic solids of revolution under nonisothermal loading

A technique for numerical analysis of the nonaxisymmetric elastoplastic stress-strain state of laminated isotropic and cylindrically orthotropic bodies of revolution under nonisothermal loading with allowance for its history is stated. The strain of isotropic materials is described by the equations of the theory of strain along small-curvature trajectories, while Hooke's law is used to describe the strain of orthotropic materials. The necessity of accounting for the loading history is shown by an example of a nonaxisymmetrically heated sandwich solid of revolution. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 2, pp. 83–90, February, 2000.     

On two approaches to determining the axisymmetric elastoplastic stress-strain state of laminated shells made of isotropic and transversely isotropic bimodulus materials

The paper compares two approaches to determining the axisymmetric elastoplastic stress-strain state of laminated shells made of isotropic and transversely isotropic materials with different elastic moduli in tension and compression. The approaches use different nonlinear constitutive equations describing the elastic deformation of the transversally isotropic bimodulus materials. Both approaches employ the theory of deformation along paths of small curvature and the Kirchhoff-Love hypothesis for the whole laminate to describe the deformation of the isotropic materials. The problem is solved by the method of successive approximations. The solutions of specific problems obtained by the two approaches are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 59–69, June 2008.     

直角坐标下横观各向同性饱和半空间体动力响应问题的解析解

基于双重Fourier变换技术，成功求解了直角坐标系下，横观各向同性弹性饱和多孔介质的三维Biot动力方程，得到了以固体骨架位移分量和孔隙流体压力为基本未知量的积分形式一般解．进而，用一般解给出了饱和介质的总应力分量表达式。在此基础上，研究了在任意分布的表面竖向和水平谐振力作用下，横观各向同性饱和半空间体的动力响应问题。数值结果表明，采用各向同性饱和介质的动力学模型，不能准确描述具有明显各向异性特性的饱和土地基的动力性能。     

各向同性和横观各向同性材料的统一点力解

本文根据横观各向同性弹性力学的通解获得了无限体的点力解，由它可以直接退化到各向同性情形的Ｋｅｌｖｉｎ解，利用这个点力解编制的边界元法程序，适用于横观各向同性材料也适用于各向同性材料，因此是真正的统一点力解。还用边界元法计算了两个数值例题。     

基于横观各向同性超弹性理论的短纤维增强橡胶本构模型的建立与应用Establishment and application of short fiber reinforced rubber constitutive model based on transversely isotropic hyperelastic theory

提出了一种能够表征短纤维增强橡胶的横观各向同性超弹性本构模型,并结合试验体系,对其在数值分析中的应用方法和效果进行了研究。基于连续介质力学理论,建立了横观各向同性材料的应变能函数,推导得到不同变形形式下的应力应变关系,给出材料参数辨识试验方法,并成功应用于某短纤维增强橡胶测试中,得到表征其超弹性特性的相关材料参数。利用有限元软件ANSYS对不同纤维排布方向的单轴拉伸和平行纤维方向的平面拉伸进行仿真计算,并对比相应试验数据,以验证材料参数的可靠性。最后基于已验证的本构模型,建立了某铣槽装备减振环仿真模型,并对其进行了校核计算。研究结果表明,本文提出的本构模型能够有效表征短纤维增强橡胶的静态力学特性并且方便嵌入现有的有限元软件中,具有材料参数少、测试简便和结果准确等特点,工程实用性强。     

Strip yield zones around ring-shaped crack in transversely isotropic thick layer

A ring-shaped crack under uniform load in an infinitely long elastic–perfectly plastic thick layer is considered. The problem is formulated for a transversely isotropic material by using integral transform technique. Due to the geometry of the configuration, Hankel integral transform technique was chosen and the problem was reduced to a singular integral equation which is solved numerically by using Gaussian Quadrature Formulae and the values were evaluated at discrete points. The plastic zone widths were obtained by using the plastic strip model after stress intensity factors were obtained. Numerical results are plotted for various ring-shaped crack sizes and transversely isotropic materials. It was found that the width of the plastic zone at the inner edge of the crack was greater than the outer one.     

横观各向同性材料的三维断裂力学问题

从三维横观各向同性材料弹性力学理论出发, 使用Hadamard有限部积分概念, 导出了三维状态下单位位移间断(位错)集度的基 本解. 在此基础上, 进一步运用极限理论, 将任意载荷作用下, 三维无限大横观各向 同性材料弹性体中, 含有一个位于弹性对称面内的任意形状的片状裂纹问题, 归结为求 解一组超奇异积分方程的问题. 通过二维超奇异积分的主部分析方法, 精确地求得了裂纹前沿光滑点附近的应力奇异指数和奇异应力场, 从而找到了以裂纹表面位移间断表示的应力强度因子表达式及裂纹局部扩展所提供 的能量释放率. 作为以上理论的实际应用，最后给出了一个圆形片状裂纹问题 的精确解例和一个正方形片状裂纹问题的数值解例. 对受轴对称法向均布载荷作用下圆形片状裂纹问题, 讨论了超奇异积分方程的精确求解方法, 并获得了位移间断和应力强度因子的封闭解, 此结果与现有理论解完全一致.     

层状横观各向同性地基上异性矩形薄板的弯曲解析解

选用更具广泛性的层状横观各向同性弹性地基模型,来分析四边自由各向异性矩形地基板的弯曲解析解。先基于直角坐标下横观各向同性体的静力胡海昌通解,借助双重傅里叶变换及矩阵传递法,获得层状横观各向同性地基的静力位移场和应力场;然后将异性薄板的弯曲控制方程,与基于层状横观各向同性弹性地基的位移解建立的板与地基变形协调方程相结合,先按对称性分解,再用三角级数法,得出层状横观各向同性弹性地基上四边自由各向异性矩形薄板的弯曲解析解,包括地基反力、板的挠度及板的内力的解析表达式。克服了数值法的弊端,取消了对地基反力的假设,且避免了矩阵指数函数的计算;同时考虑了地基的层状性及板和地基的各向异性,从而得到板的内力及地基反力更切实际的分布规律。算例结果与文献的有限元结果吻合良好,证明本文方法是切实可行的。     

压电界面裂纹裂尖强度因子的显式计算公式

对常见横观各向同性压电材料(TIP)中界面裂纹的裂纹面与压电材料的极化方向成任意夹角的一般情况进行了研究,通过推导得到了计算裂尖强度因子的显式外推公式,同时给出了裂纹面与极化方向垂直的典型情况下的外推公式.这些显式计算公式为常见数值方法如有限元法及边界元法在压电材料断裂力学中的应用提供了便利.     

Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground

The non-axisymmetrical vibration of elastic circular plate resting on a layered transversely isotropic saturated ground was studied.First,the 3-d dynamic equations in cylindrical coordinate for transversely isotropic saturated soils were transformed into a group of governing differential equations with 1-order by the technique of Fourier ex- panding with respect to azimuth,and the state equation is established by Hankel integral transform method,furthermore the transfer matrixes within layered media are derived based on the solutions of the state equation.Secondly,by the transfer matrixes,the general solutions of dynamic response for layered transversely isotropic saturated ground excited by an arbitrary harmonic force were established under the boundary conditions, drainage conditions on the surface of.ground as well as the contact conditions.Thirdly, the problem was led to a pair of dual integral equations describing the mixed boundary- value problem which can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure easily.At the end of this paper,a numerical result concerning vertical and radical displacements both the surface of saturated ground and plate is evaluated.     

Experimental and theoretical analysis of the deformation of transversely isotropic plates under creep conditions

This paper describes the results of calculations and experiments on the torsion of plates made of isotropic and transversely isotropic VT-20 and 1163T alloys with low resistance to creep strain in the direction perpendicular to the median surface. The numerical simulation results for plates of different thicknesses related to the class of rigid and flexible plates are compared using the pure bending theory and the finite element method. It is found that the curvature values are smaller in the case of deformation of a plate made of anisotropic material into a sign-variable saddle surface than in the case of a plate of isotropic material. The calculation in the assumption of pure bending provides an upper bound of the curvature difference in the deformation of plates made of transversely isotropic and isotropic materials.     

Numerical investigation of the plastic stress-strain state of laminated shells in axisymmetric deformation processes with small-curvature trajectories and allowance for geometric nonlinearity

Within the framework of the Kirchhoff-Love hypothesis, a procedure is developed for numerical investigation of the axisymmetric plastic stress-strained state of laminated shells with allowance for geometric nonlinearity. The process of deformation of isotropic materials is described by using the theory of deformation with small-curvature trajectories, while Hooke’s law is used to describe the deformation of orthotropic materials. The effect of inelastic complex deformation of two isotropic layers on an orthotropic layer is studied in an example of a three-layer shell. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 32, No. 8, pp. 80–86, August, 1996.