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<p>To address the singularity issues caused by additional degrees of freedom in standard generalized finite elements and the volumetric locking problem that tends to occur when the incompressibility of materials increases, this paper proposes a generalized finite element solid element based on displacements and displacement gradients (referred to as DGG-Solid-H8). This element uses physically meaningful displacements and their gradients as nodal parameters in the generalized finite element formulation and constructs enriched functions using Taylor expansions over the nodal support domains. The DGG-Solid-H8 element effectively resolves the volumetric locking and singularity problems by constructing a continuous strain field with displacement gradients as nodal parameters, and it can pass the patch test and zero-energy mode test. Numerical examples show that under certain mesh conditions, the DGG-Solid-H8 element can easily achieve a calculation accuracy of 99%, demonstrating good robustness. Moreover, the proposed construction method of the DGG-Solid-H8 element has excellent scalability, providing new theoretical guidance for the finite element analysis of planar, beam, and shell structures.</p>

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A high-performance 8-node hexahedral solid element with gradient nodal parameters

  • 期刊论文

  • 发表日期：

    2026年1月26日

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  • Guanxin Huang,
  • Mingxuan Li,
  • Hangxing Li,
  • Xin Chen,
  • Zhijun Yang

摘要

To address the singularity issues caused by additional degrees of freedom in standard generalized finite elements and the volumetric locking problem that tends to occur when the incompressibility of materials increases, this paper proposes a generalized finite element solid element based on displacements and displacement gradients (referred to as DGG-Solid-H8). This element uses physically meaningful displacements and their gradients as nodal parameters in the generalized finite element formulation and constructs enriched functions using Taylor expansions over the nodal support domains. The DGG-Solid-H8 element effectively resolves the volumetric locking and singularity problems by constructing a continuous strain field with displacement gradients as nodal parameters, and it can pass the patch test and zero-energy mode test. Numerical examples show that under certain mesh conditions, the DGG-Solid-H8 element can easily achieve a calculation accuracy of 99%, demonstrating good robustness. Moreover, the proposed construction method of the DGG-Solid-H8 element has excellent scalability, providing new theoretical guidance for the finite element analysis of planar, beam, and shell structures.