论文标题
完全的一般解决方案，用于各向同性应变梯度弹性的平衡方程
Complete general solutions for equilibrium equations of isotropic strain gradient elasticity
论文作者
论文摘要
在本文中，我们考虑了各向同性思维型菌株应变梯度弹性理论，其中平衡方程包含两个额外的长度尺度参数，并具有第四阶。对于这一理论，我们开发了Boussinesq-Galerkin（BG）和Papkovich-Neuber（PN）通用解决方案的扩展形式。获得的BG解决方案的形式可以通过单个向量函数来定义位移场，该函数遵守八阶Bi-Harmonic/bi-Helmholtz方程。溶液的开发的PN形式将位移场分别通过标准Papkovich应力函数定义和修改的Helmholtz分解提供了位移场的加性分解。建立了不同压力函数与完整定理之间的关系。举例来说，证明了应变梯度弹性中先前已知的基本解决方案，可以使用开发的PN常规溶液来得出。
In this paper, we consider isotropic Mindlin-Toupin strain gradient elasticity theory in which the equilibrium equations contain two additional length-scale parameters and have the fourth order. For this theory we developed an extended form of Boussinesq-Galerkin (BG) and Papkovich-Neuber (PN) general solutions. Obtained form of BG solution allows to define the displacement field through the single vector function that obeys the eight-order bi-harmonic/bi-Helmholtz equation. The developed PN form of the solution provides an additive decomposition of the displacement field into the classical and gradient parts that are defined through the standard Papkovich stress functions and modified Helmholtz decomposition, respectively. Relations between different stress functions and completeness theorem for the derived general solutions are established. As an example, it is shown that a previously known fundamental solution within the strain gradient elasticity can be derived by using the developed PN general solution.
