当前位置:
X-MOL 学术
›
Comput. Struct.
›
论文详情
Our official English website, www.x-mol.net, welcomes your
feedback! (Note: you will need to create a separate account there.)
A discontinuous Galerkin method based isogeometric analysis framework for flexoelectricity in micro-architected dielectric solids
Computers & Structures ( IF 4.4 ) Pub Date : 2025-01-08 , DOI: 10.1016/j.compstruc.2024.107641
Saurav Sharma, Cosmin Anitescu, Timon Rabczuk
Computers & Structures ( IF 4.4 ) Pub Date : 2025-01-08 , DOI: 10.1016/j.compstruc.2024.107641
Saurav Sharma, Cosmin Anitescu, Timon Rabczuk
Flexoelectricity, the generation of electric field in response to a strain gradient, is a universal electromechanical coupling, dominant only at small scales due to its requirement of high strain gradients. This phenomenon is governed by a set of coupled fourth-order partial differential equations (PDEs), which require C 1 continuity of the basis in finite element methods for the numerical solution. While Isogeometric analysis (IGA) has been proven to meet this continuity requirement due to its higher-order B-spline basis functions, it is limited to simple geometries that can be discretized with a single IGA patch. For complex domains, e.g., architected materials, which require more than one patch for discretization, IGA faces the challenge of C 0 continuity across the patch boundaries. Here we present a discontinuous Galerkin method-based isogeometric analysis framework, capable of solving fourth-order PDEs of flexoelectricity in the domain of truss-based architected materials. An interior penalty-based stabilization is implemented to ensure the stability of the solution. The present formulation is advantageous over the analogous finite element methods since it only requires the computation of interior boundary contributions on the boundaries of patches. As each strut can be modeled with only two trapezoid patches, the number of C 0 continuous boundaries is largely reduced. We consider four unit cells to construct the truss lattices and analyze their flexoelectric response. The truss lattices show a higher magnitude of flexoelectricity compared to the solid beam and retain this superior electromechanical response with the increasing size of the structure. This demonstrates the potential of architected materials to scale up flexoelectricity to larger scales, and achieve universal electromechanical response in meso/macro scale dielectric materials.
中文翻译:
基于间断 Galerkin 方法的微架构介电体中柔性电的等几何分析框架
挠曲电是响应应变梯度而产生电场的现象,是一种通用的机电耦合,由于其对高应变梯度的要求,仅在小尺度上占主导地位。这种现象由一组耦合的四阶偏微分方程 (PDE) 控制,在有限元方法中,数值求解需要基的 C1 连续性。虽然等几何分析 (IGA) 由于其高阶 B 样条基函数而被证明可以满足这一连续性要求,但它仅限于可以使用单个 IGA 补丁离散化的简单几何结构。对于需要多个补丁进行离散化的复杂领域,例如架构材料,IGA 面临着跨补丁边界的 C0 连续性的挑战。在这里,我们提出了一个基于非间断 Galerkin 方法的等几何分析框架,能够在基于桁架的架构材料领域求解挠曲电的四阶偏微分方程。实施基于内部罚的稳定化以确保解的稳定性。目前的公式比类似的有限元方法更有利,因为它只需要计算补丁边界上的内部边界贡献。由于每个支柱只能用两个梯形补丁进行建模,因此 C0 连续边界的数量大大减少。我们考虑四个晶胞来构建桁架晶格并分析它们的挠曲电响应。与实心梁相比,桁架晶格显示出更高的挠曲电强度,并随着结构尺寸的增加而保持这种卓越的机电响应。 这证明了建筑材料的潜力,可以将挠曲电放大到更大规模,并在中观/宏观尺度介电材料中实现通用的机电响应。
更新日期:2025-01-08
中文翻译:
基于间断 Galerkin 方法的微架构介电体中柔性电的等几何分析框架
挠曲电是响应应变梯度而产生电场的现象,是一种通用的机电耦合,由于其对高应变梯度的要求,仅在小尺度上占主导地位。这种现象由一组耦合的四阶偏微分方程 (PDE) 控制,在有限元方法中,数值求解需要基的 C1 连续性。虽然等几何分析 (IGA) 由于其高阶 B 样条基函数而被证明可以满足这一连续性要求,但它仅限于可以使用单个 IGA 补丁离散化的简单几何结构。对于需要多个补丁进行离散化的复杂领域,例如架构材料,IGA 面临着跨补丁边界的 C0 连续性的挑战。在这里,我们提出了一个基于非间断 Galerkin 方法的等几何分析框架,能够在基于桁架的架构材料领域求解挠曲电的四阶偏微分方程。实施基于内部罚的稳定化以确保解的稳定性。目前的公式比类似的有限元方法更有利,因为它只需要计算补丁边界上的内部边界贡献。由于每个支柱只能用两个梯形补丁进行建模,因此 C0 连续边界的数量大大减少。我们考虑四个晶胞来构建桁架晶格并分析它们的挠曲电响应。与实心梁相比,桁架晶格显示出更高的挠曲电强度,并随着结构尺寸的增加而保持这种卓越的机电响应。 这证明了建筑材料的潜力,可以将挠曲电放大到更大规模,并在中观/宏观尺度介电材料中实现通用的机电响应。