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首页> 外文期刊>International Journal of Solids and Structures >Variational formulations and a consistent finite-element procedure for a class of nonlocal elastic continua
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Variational formulations and a consistent finite-element procedure for a class of nonlocal elastic continua

机译：一类非局部弹性连续体的变分公式和一致的有限元程序

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摘要

The structural boundary-value problem in the context of nonlocal (integral) elasticity ana quasi-static loads is considered in a geometrically linear range. The nonlocal elastic behaviour is described by the so-called Eringen model in which the nonlocality, ties in the constitutive relation. The diffusion processes of the nonlocality are governed by an integral relation containing a recently proposed symmetric spatial weight function expressed in terms of an attenuation function. A firm variational basis to the nonlocal model is given by providing the complete set of variational formulations, composed by ten functionals with different combinations of the state variables. In particular the nonlocal counterpart of the classical principles of the total potential energy, complementary energy and mixed Hu-Washizu principle and Hellinger-Reissner functional are recovered. Some examples concerning a piecewise bar in tension are provided by using the Fredholm integral equation and the proposed nonlocal FEM.
机译：在几何线性范围内考虑非局部（整体）弹性和准静态载荷情况下的结构边界值问题。非局部弹性行为由所谓的Eringen模型描述，其中非局部性与本构关系相关。非局部性的扩散过程由包含最近提出的对称空间权重函数的积分关系控制，该对称空间权重函数用衰减函数表示。通过提供由十种具有状态变量的不同组合的函数组成的完整的变分公式集，可以为非局部模型提供牢固的变分基础。特别是，恢复了总势能，互补能以及混合的Hu-Washizu原理和Hellinger-Reissner泛函的经典原理的非局部对应关系。通过使用Fredholm积分方程和建议的非局部FEM，提供了一些有关拉力分段的示例。

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