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theorem
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  定理
    Application of Chien's Theorem to the Establishing of General Variational Principle in Polar Elasticity of Finite Deformation
    钱氏定理在有限变形极矩弹性力学广义变分原理的应用
短句来源
    Applications of the Reciprocal Theorem to Solving the Equations of the Deflection Surface of the Rectangular Plates with Various Edge Conditions
    应用功的互等定理求解具有复杂边界条件的矩形板的挠曲面方程
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    On Equivalents of the Reciprocal Theorem to Superposition Principles
    关于功的互等定理与叠加原理的等价性
短句来源
    Toupin-Berdichevskii Theorem Can't Be Considered as a Mathematical Expression of Saint- Venant's Principle
    Toupin-Бердичевский定理不能作为圣维南原理的数学表达
短句来源
    THEOREM OF THE DISPLACEMENT OF A PARTICLE
    质点的位移定理
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  原理
    On Equivalents of the Reciprocal Theorem to Superposition Principles
    关于功的互等定理与叠加原理的等价性
短句来源
    Toupin-Berdichevskii Theorem Can't Be Considered as a Mathematical Expression of Saint- Venant's Principle
    Toupin-Бердичевский定理不能作为圣维南原理的数学表达
短句来源
    Application of the Mixed Energy Theorem to Setting up the Bending Admissible Displacement of Rectangular Plates
    应用混合能量原理构造矩形板的弯曲容许位移
短句来源
    Further Study of the Equivalent Theorem of Hellinger_ Reissner and Hu_Washizu Variational Principles
    再论Hellinger-Reissner原理与Hu-Washizu原理之等价性
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    Some Related Problems and the Relationship Between the Theorem of Kinetic Energy and the Function Theorem
    动能定理与功能原理的关系及其有关问题
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  “theorem”译为未确定词的双语例句
    On the Free Energy and Variational Theorem of Elastic Problem in Thermal Shock
    关于热冲击弹性问题的自由能及变分原理
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    APPLICATION OF MILES-HOWARD THEOREM TO STUDY THE INSTABILITY OF ATMOSPHERIC GRAVITY WAVES ON A HETEROGENEOUS ORTHOGONAL SHEAR FLOW
    APPLICATION OF MILES-HOWARD THEOREM TO STUDY THE INSTABILITY OF ATMOSPHERIC GRAVITY WAVES ON A HETEROGENEOUS ORTHOGONAL SHEAR FLOW
短句来源
    Reciprocal Theorem Method for the Forced Vibration of Elastic Thick Rectangular Plates
    弹性厚矩形板受迫振动的功的互等定理法
短句来源
    The Analysis of Natural Frequency of Rectangular Plates with Four Fixed Edges by Reciprocal Theorem
    固支矩形板固有频率分析的功的互等定理法
短句来源
    Inverse Noether's Theorem and Inverse Problem of Lie Symmetries forHolonomic Nonconservative Mechanical Systems
    完整非保守力学系统的Noether逆定理与Lie对称性逆问题
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  theorem
In the case of 3-dimensional commutative algebras a new proof of a recent theorem of Katsylo and Mikhailov about the 28 bitangents to the associated plane quartic is given.
      
If the additive group of complex numbers acts algebraically on a normal affine variety, then the associated ring of invariants need not be finitely generated, but is an ideal transform of some normal affine algebra (Theorem 1).
      
If the variety is a complex affine space and the ring of invariants is isomorphic to a polynomial ring, then the action is conjugate to a translation (Theorem 3).
      
On the other hand, there is a locally trivialGa-action on a normal affine variety with nonfinitely generated ring of invariants (Theorem 2).
      
As an application of the results we prove a generalization of Chevalley's restriction theorem for the classical Lie algebras.
      
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By using the description method of comoving coordinates and the geometric field theory developed in the previous part of this paper (Acta Mechanica Sinica (2) 1979, 107-117), the fundamental equations and the energy principles for finite polar elasticity have been established. These make improvements to Fraeijs de Veubeke's formulation (1972) of new variational principle which based on polar decomposition theorem. Engineering applications are shown for large deflection of beam and Koiter's solution (1973)...

By using the description method of comoving coordinates and the geometric field theory developed in the previous part of this paper (Acta Mechanica Sinica (2) 1979, 107-117), the fundamental equations and the energy principles for finite polar elasticity have been established. These make improvements to Fraeijs de Veubeke's formulation (1972) of new variational principle which based on polar decomposition theorem. Engineering applications are shown for large deflection of beam and Koiter's solution (1973) for second order effect in simple shear.

在[1]文中建立了可变形体三维空间有限变形几何场论。在本文中进一步建立可变体的运动学公式,说明拖带系(Comoving Coordinates)描述法是 Euler刚体动坐标系描述法在变形体力学的自然推广。在此基础上建立了有体矩作用情况下有限变形弹性力学的基本方程和能量原理。和 (1970)、 Fraeijs de Veubeke(1972)、 Koiter(1973)等提出的有限变位新变分原理相比,在工程实用价值有显著提高。文中并以梁的大挠度方程和Koiter关于简单剪切二阶效应之解为例说明原理的应用。 新理论在应用上已可以取代古典非线性弹性力学的地位。

This paper presents an approximate method to obtain the maximum residual deformation for impulsively loaded rigid-plastic structures. It is proved that the vanishing of the first variation of the functional J is equivalent to all the equations which should be satisfied in the dynamics of rigid-plastic continua. Under special conditions this generalized variational principle coincides with the previous two extremum principles[2,3]. We have applied our variational principle to the simply supported beam loaded...

This paper presents an approximate method to obtain the maximum residual deformation for impulsively loaded rigid-plastic structures. It is proved that the vanishing of the first variation of the functional J is equivalent to all the equations which should be satisfied in the dynamics of rigid-plastic continua. Under special conditions this generalized variational principle coincides with the previous two extremum principles[2,3]. We have applied our variational principle to the simply supported beam loaded by rectangular pulse and found that the results are much closer to the exact solution than those from the upper bound theorem[4] and lower bound theorem[5] in the rigid-plastic dynamics.

本文给出一个利用一般变分原理来求刚塑性结构在冲击载荷作用下最大残余变形的近似方法.证明了泛函J的一次变分为零相当于满足刚塑性体动力学的全部方程.在特殊情况下,新的一般变分原理将与已有的两个极值原理~[2,3]相重合.通过简支梁受均布矩形冲击载荷作用来作为实例应用,说明本法与已有的刚塑性动力学的上限~[4]与下限~[5]定理相比,更接近于完全解的结果.

Let the axisymmetric loads formed by Mindlin's Point forces be distributed along the Z-axis in (0, L) of the elastic half-space. In addition to Boussinesq's solution, We can reduce the problem with the following boundary conditions1.Z=0,r≠0,σz=τrz=02.0≤z≤L,U(e,z)=a-e,(1≥e/a≈1)3.P=-2π[a∫Lτry(a,z)dz+∫0arσ(r,L)dr](1)to a Fredholm integral equation of the first kind.A theorem of error estimation for the approximate solution of such an equtaion is presented. Applied to piles analysis, this method probably has...

Let the axisymmetric loads formed by Mindlin's Point forces be distributed along the Z-axis in (0, L) of the elastic half-space. In addition to Boussinesq's solution, We can reduce the problem with the following boundary conditions1.Z=0,r≠0,σz=τrz=02.0≤z≤L,U(e,z)=a-e,(1≥e/a≈1)3.P=-2π[a∫Lτry(a,z)dz+∫0arσ(r,L)dr](1)to a Fredholm integral equation of the first kind.A theorem of error estimation for the approximate solution of such an equtaion is presented. Applied to piles analysis, this method probably has several advantages over that by. R. Butterfield et al. i. e., the integral equation obtained is one-dimensional nonsiagular; the effect of initial stresses is taken into account; the unknown settlement funtion at the surface of the pile need not be prescribed; three-dimensional stress state in compressible piles is taken into account.

将由Mindlin集中力组成的轴对称载荷沿弹性半空间z轴[0,L]内分布,并迭加Boussinesq的解,就能使边界条件为1.Z=0,r≠0,σz=τrz=02.0≤z≤L,U(e,z)=a-e,(1≥e/a≈1)3.P=-2π[a∫Lτry(a,z)dz+∫0arσ(r,L)dr](1)的圆柱嵌入半空间的三维问题归结为一Fredholm第一种积分方程.本文给出了Fredholm第一种积分方程近似解误差估计的一个定理. 将本文所论述的方法,用于桩的分析,较R.Butterfield等人的方法为优越,即所得到积分方程是一维非奇异的、能考虑初应力的影响、不需要预先假定沉陷函数,并且考虑了可压缩桩中的三维应力状态.

 
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