As there are different computational methods for simulating problems in generalized mechanics, we present simple applications and their closed-form solutions for verifying a numerical implementation. For such a benchmark, we utilize these analytical solutions and examine three-dimensional numerical simulations by the finite element method (FEM) using IsoGeometric Analysis (IGA) with the aid of open source codes, called tIGAr, developed within the FEniCS platform. A study for the so-called wedge forces and double tractions help to comprehend their roles in the displacement solution as well as examine the significance by comparing to the closed form solutions for given boundary conditions. It is found that numerical results are in a good agreement with the analytical solutions if wedge forces and double tractions are considered. It is also presented how the wedge forces become necessary in order to maintain equilibrium in strain gradient materials.

中文翻译：

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通过解析解验证应变梯度弹性计算

由于模拟广义力学中的问题有不同的计算方法，我们提出了简单的应用程序及其封闭形式的解决方案，以验证数值实现。对于这样的基准，我们利用这些解析解，并借助在 FEniCS 平台内开发的名为 tIGAr 的开源代码，通过有限元方法 (FEM) 使用等几何分析 (IGA) 检查三维数值模拟。对所谓的楔力和双牵引力的研究有助于理解它们在位移解中的作用，并通过与给定边界条件的封闭形式解进行比较来检查其重要性。发现如果考虑楔力和双牵引力，数值结果与解析解具有很好的一致性。