关于板的动力学的最小转换能量原理和最小值原理
Principles of Minimum Transformed Energy and Minimum Principles for Dynamics of Plates
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摘要: 本文首先通过Laplace变换导出了关于具有三个广义位移并考虑转动惯量效应时各向异性的线弹性板在动力学中的转换虚功原理和三个最小转换能量原理及其在原空间时间域中用原函数表示的对应形式,然后通过引进相容权函数的集合推导出关于空间时间域的三个最小值原理.在上述两组最小值原理中各有两个均为板在静力学中最小势能原理和最小余能原理的推广形式;而另一个最小值原理,在静力学中便没有对应形式.Abstract: In the present paper,we first by Laplace transform present a derivation of principle of transformed virtual work,three principles of minimum transformed energy with influence of rotatory enertiafor dynamics of anisotropic linear elastic plates with three generalized displacements.Moreover,the forms with the original in place-time domain corresponding these variational principles are presented.Then by the introduction of the set of admissible weight functions the three minimum principles for the original place-time domain are derived.In each of the preceding groups of the variational principles there are two which are the dynamic counterparts to the static principles of minimum potetial energy and minimum complementary energy;the other principles are formulated in terms of the internal force alone,but have no counterpart in elastostatics of plates.
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[1] Mindlin,K.D.,Influence of rotatory and shear on flexural motion of isotropic elastic plates,Journal of Applied Mechanics,18,1(1951),35. [2] 胡海昌,《弹性力学的变分原理及其应用》,科学出版社(1981),465. [3] Gurtin,M.E.,Variational Principles for linear elastodynamics,Archive for Rational Mechanics and Analysis,16,1(1964),34. [4] 南京工学院数学教研组,《工程数学,积分变换》,人民教育出版社(1981).34. [5] Reiss,R.,Minimum principles for linear elastodynamics,Journal of Elasticity,8,1(1978),35.
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