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1.
The propagation of the energy of nonlinearly elastic plane waves in a Murnaghan material is simulated on a computer. The velocity of energy propagation is found in an explicit form. A procedure of determining the critical values of the time and space coordinates for the given material is described. The resultant plots are discussed and analyzed 相似文献
2.
Change of type in the governing equations of equilibrium is examined in the context of a base neo-Hookean response augmented
with unidirectional reinforcing that is characterized by a single additional constitutive parameter for strength of reinforcement.
Plane deformations interpreted in terms of both local and global plane strain are considered. Loss of ordinary ellipticity
is found to occur for sufficiently large strength of reinforcement under sufficiently severe deformation which necessarily
involves contraction in the reinforcing direction. Loss of ellipticity in local plane strain is easily characterized, and
its incipient breakdown is associated with the possible emergence of surfaces of weak discontinuity with orientation normals
in the reinforcing direction. Loss of ellipticity in global plane strain is given a two-dimensional manifold characterization
in a space involving 2 deformation parameters and the strength of reinforcing parameter. Orientation normals for the associated
surfaces of weak discontinuity at incipient breakdown do not in general conform to the reinforcing direction.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
3.
振动系统动力学设计迭代算法及解的存在性讨论 总被引:1,自引:0,他引:1
振动系统动力学设计被抽象为高维广义非线性特征值反问题。若系统构成以可变参数表示,则可构造一个非线性多元函数。基于多元函数极小原理,提出了一套求解这一特征值反问题的迭代算法。该算法不受系统给定阶数和给定方向的限制,也适用于具有重特征值的退化情况,系统或结构的构成材料可以是任意的。文中同时讨论了解的存在条件,且以显式表达,可方便地应用于工程实际。结合某直升机旋翼桨叶的动力学设计,给出了应用的数值算例。大量数值仿真结果及应用实践表明,本文算法具很好的收敛性,并有较高的计算精度。 相似文献
4.
在传统的关于液固撞击的激波理论模型中,引入矢量分析的方法,考虑到高速度撞击时,液体运动的迁移性和非线性效应,以及固体的可变形性,提出了一个适用于高撞击马赫数的无量纲激波理论模型。该模型能够计算出所有撞击参数,计算结果与实验数据吻合良好。模型所导出的计算方法物理意义明确,简明准确,适用范围宽广,且便于工程上制成图表查用。 相似文献
5.
Continuous and integrable solutions and one-to-one relationships between boundary forces and displacements are found through the direct integration of the differential equations of the plane elastic problem for a half-plane with boundary conditions for either forces or displacements or with mixed boundary conditions. The necessary equilibrium conditions for forces and the compatibility conditions for displacements that ensure the correctness of the solutions are formulated 相似文献
6.
A new technique is proposed for solving the three-dimensional antisymmetric elastic problem for a thick-walled shell of finite length. The boundary-value problem is reduced to a system of one-dimensional singular integral equations. Characteristic stresses are calculated 相似文献
7.
Gao Yongxin 《应用数学和力学(英文版)》1996,17(6):569-576
In this paper, the author uses the methods in [1, 2] to study the existence of solutions of three point boundary value problems for nonlinear fourth order differential equation.% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaCa% aaleqabaGaaiikaiaaisdacaGGPaaaaOGaeyypa0JaaGOKbiaacIca% caWG0bGaaiilaiaadMhacaGGSaGabmyEayaafaGaaiilaiqadMhaga% GbaiaacYcaceWG5bGbaibacaGGPaaaaa!4497!\[y^{(4)} = f(t,y,y',y',y')\] with the boundary conditions% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiGaaqaabe% qaaiaadEgacaGGOaGaamyEaiaacIcacaWGHbGaaiykaiaacYcaceWG% 5bGbauaacaGGOaGaamyyaiaacMcacaGGSaGabmyEayaagaGaaiikai% aadggacaGGPaGaaiilaiqadMhagaGeaiaacIcacaWGHbGaaiykaiaa% cMcacqGH9aqpcaaIWaGaaiilaiaadIgacaGGOaGaamyEaiaacIcaca% WGIbGaaiykaiaacYcaceWG5bGbayaacaGGOaGaamOyaiaacMcacaGG% PaGaeyypa0JaaGimaaqaaiqadMhagaqbaiaacIcacaWGIbGaaiykai% abg2da9iaadkgadaWgaaWcbaGaaGymaaqabaGccaGGSaGaam4Aaiaa% cIcacaWG5bGaaiikaiaadogacaGGPaGaaiilaiqadMhagaqbaiaacI% cacaWGJbGaaiykaiaacYcaceWG5bGbayaacaGGOaGaam4yaiaacMca% caGGSaGabmyEayaasaGaaiikaiaadogacaGGPaGaaiykaiabg2da9i% aaicdaaaGaayzFaaaaaa!7059!\[\left. \begin{gathered} g(y(a),y'(a),y'(a),y'(a)) = 0,h(y(b),y'(b)) = 0 \hfill \\ y'(b) = b_1 ,k(y(c),y'(c),y'(c),y'(c)) = 0 \hfill \\ \end{gathered} \right\}\] For the boundary value problems of nonlinear fourth order differential equation% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaCa% aaleqabaGaaiikaiaaisdacaGGPaaaaOGaeyypa0JaaGOKbiaacIca% caWG0bGaaiilaiaadMhacaGGSaGabmyEayaafaGaaiilaiqadMhaga% GbaiaacYcaceWG5bGbaibacaGGPaaaaa!4497!\[y^{(4)} = f(t,y,y',y',y')\] many results have been given at the present time. But the existence of solutions of boundary value problem (*). (**) studied in this paper has not been involved by the above researches. Morcover, the corollary of the important theorem in this paper, i. e. existence of solutions of the boundary value problem of equation (*) with the following boundary conditions.% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGHb% WaaSbaaSqaaiaaicdaaeqaaOGaamyEaiaacIcacaWGHbGaaiykaiab% gUcaRiaadggadaWgaaWcbaGaaGymaaqabaGcceWG5bGbauaacaGGOa% GaamyyaiaacMcacqGHRaWkcaWGHbWaaSbaaSqaaiaaikdaaeqaaOGa% bmyEayaagaGaaiikaiaadggacaGGPaGaey4kaSIaamyyamaaBaaale% aacaaIZaaabeaakiqadMhagaGeaiaacIcacaWGHbGaaiykaiabg2da% 9iaadMhadaWgaaWcbaGaaGimaaqabaGccaGGSaGaamOyamaaBaaale% aacaaIWaaabeaakiaadMhacaGGOaGaamOyaiaacMcacqGHRaWkcaWG% IbWaaSbaaSqaaiaaikdaaeqaaOGabmyEayaagaGaaiikaiaadkgaca% GGPaGaeyypa0JaamyEamaaBaaaleaacaaIXaaabeaaaOqaaiqadMha% gaqbaiaacIcacaWGIbGaaiykaiabg2da9iaadMhadaWgaaWcbaGaaG% OmaaqabaGccaGGSaGaam4yamaaBaaaleaacaaIWaaabeaakiaadMha% caGGOaGaam4yaiaacMcacqGHRaWkcaWGJbWaaSbaaSqaaiaaigdaae% qaaOGabmyEayaafaGaaiikaiaadogacaGGPaGaey4kaSIaam4yamaa% BaaaleaacaaIYaaabeaakiqadMhagaGbaiaacIcacaWGJbGaaiykai% abgUcaRiqadogagaGeaiaacIcacaWGJbGaaiykaiabg2da9iaadMha% daWgaaWcbaGaaG4maaqabaaaaaa!7DF7!\[\begin{gathered} a_0 y(a) + a_1 y'(a) + a_2 y'(a) + a_3 y'(a) = y_0 ,b_0 y(b) + b_2 y'(b) = y_1 \hfill \\ y'(b) = y_2 ,c_0 y(c) + c_1 y'(c) + c_2 y'(c) + c'(c) = y_3 \hfill \\ \end{gathered} \] has not been dealt with in previous works. 相似文献
8.
Experimental data for simple tension suggest that there is a power–law kinematic relationship between the stretches for large
classes of slightly compressible (or almost incompressible) non-linearly elastic materials that are homogeneous and isotropic.
Here we confine attention to a particular constitutive model for such materials that is of generalized Varga type. The corresponding
incompressible model has been shown to be particularly tractable analytically. We examine the response of the slightly compressible material
to some nonhomogeneous deformations and compare the results with those for the corresponding incompressible model. Thus the effects of slight compressibility
for some basic nonhomogeneous deformations are explicitly assessed. The results are fundamental to the analytical modeling
of almost incompressible hyperelastic materials and are of importance in the context of finite element methods where slight
compressibility is usually introduced to avoid element locking due to the incompressibility constraint. It is also shown that
even for slightly compressible materials, the volume change can be significant in certain situations.
相似文献
9.
模型复合材料弹塑性界面应力分析 总被引:9,自引:0,他引:9
由纤维增强弹塑性基体所产生的界面具有弹塑性力学行为。考虑到一般材料的塑性变形都遵循幂硬化规律,对模型复合材料的界面进行弹性和应变硬化状态下的变形规律及其应力分析。以纤维拔出试验为研究模型,将界面分成弹性区和塑性区。利用界面应力剪滞理论,分别建立弹性区和塑性区的界面力学基本方程。选择适当的位移函数满足基本方程及埋入纤维的边界条件,再按位移函数求出弹性区和塑性区的界面剪应力。推导出平均界面剪应力与纤维 相似文献
10.
利用复变函数法、多极坐标移动技术及傅立叶级数展开求解二维直角平面内圆形弹性夹杂对稳态入射平面SH波的散射问题。首先写出直角平面内不含夹杂时的入射波场和反射波场;其次建立直角平面内含夹杂时夹杂外的散射波解和夹杂内的驻波解,并利用叠加原理写出问题的总波场,借助夹杂边界处应力和位移的连续条件建立求解散射波解和驻波解中未知系数的无穷代数方程组并求解,通过算例具体讨论了直角平面水平边界点的位移幅度比和夹杂边界处径向应力集中系数随不同无量纲波数、入射角及圆孔位置的变化情况,结果表明了算法的有效实用性。 相似文献
11.
12.
The basic inverse boundary value problem of aerohydrodynamics for a two-element airfoil is analytically and numerically solved in the complete formulation. The problems of designing biplane airfoils and an airfoil with a trailing-edge flap or leading edge flap (slat) are solved for a given distribution over the unknown contours of the velocity or the pressure as a function of the contour arc abscissa of the airfoils which depends on a finite number of the parameters. 相似文献
13.
V. P. Radchenko D. V. Shapievskii 《Journal of Applied Mechanics and Technical Physics》2008,49(3):478-483
A mathematical model is proposed to describe the experimentally observed creep effect on the instantaneous elastic deformation
of physically nonlinear elastic microinhomogeneous materials. Using a structural model of the medium, it is shown that, during
unloading of a sample after creep at constant stress, the elastic strain can be both larger and smaller than the elastic strain
during loading. It is shown that calculation results for a biocomposite material are in good agreement with experimental data.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 157–163, May–June, 2008. 相似文献
14.
This paper investigates pitch motion and in orbital plane elastic vibration of a spacecraft with a flexible beam type appendage undergoing prescribed slew maneuver. The governing equations are transformed into a standard quasi-linear form, and then solved by Butenin's variation of parameters approach. Validity of the analytical solutions is assessed over a range of system parameters and initial conditions by comparing them with the results of numerical integration. The results show that they are very good approximations and provide extensive insight into the dynamical response of the system. 相似文献
15.
González Rogelio Vázquez Giudici Mauro Ponzini Giansilvio Parravicini Guido 《Transport in Porous Media》1997,26(3):339-371
The differential system (DS) method for the identification of transmissivity and storativity is applied to a confined isotropic aquifer in transient conditions. The data that are required for the identification are the piezometric heads and the source terms, together with the value of transmissivity at a single point only, which is the only parameter value needed a priori. In particular, no a priori knowledge of storativity is needed and, moreover, the identification of transmissivity does not depend upon storativity. The DS method yields the internode transmissivities necessary for the conservative finite differences models in a natural way, because it identifies transmissivities along the internodal segments, so that a well-known formula can be applied that bypasses the difficulty of finding an equivalent cell transmissivity and an averaging scheme. In addition, the DS method takes into account several different flows all over the aquifer, so that the identified parameters are to a certain degree global andflow independent. Moreover, the method allows for a piecemeal identification of the parameters, thus keeping away from the regions where wells are pumping so that a two-dimensional model can be used throughout. We test the applicability of the DS method with noisy data by means of numerical synthetic examples and compare the identified internode transmissivities with the reference values. We use the identified parameters to forecast the behaviour of the aquifer under different exploitation and boundary conditions and we compare the forecast piezometric heads, their gradients and the associated fluxes with those computed with the reference parameters. 相似文献
16.
17.
We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational forces. The higher-order derivative of unknown S exists in the sense of local weak derivatives since it may be not summable over the original open domain. The existence proof is valid in the one-dimensional case. 相似文献
18.
We consider a linearly elastic shell with an “elliptic” middle surface, clamped along a portion of its lateral face and subjected
to body forces. Under weak regularity assumptions on the middle surface, we prove that the space of linearized inextensional
displacements is reduced to zero, by using unique continuation results. Consequently, when the thickness of the shell goes
to zero, the limit of the average with respect to the thickness of the three-dimensional displacement vector solves the “generalized
membrane” shell model, according to the terminology introduced by P.G. Ciarlet and the first author.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
19.
THEEXISTENCEOFPERIODICSOLUTIONSFORACLASSOFFUNCTIONALDIFFERENTIALEQUATIONSANDTHEIRAPPLICATIONZhaoJie-min(赵杰民);HuangKe-lei(黄克累)... 相似文献
20.
赵为礼 《应用数学和力学(英文版)》1991,12(11):1105-1116
In this paper the existence of solutions of the singularly perturbed boundary valueproblems on infinite interval for the second order nonlinear equation containing a smallparameterε>0 :is examined,whereα_i,βare constants,and i=0,1 .Moreover,asymptoticestimates of the solutions for the above problems are given. 相似文献