This contribution presents an alternative stabilization technique for the virtual element method (VEM) based on reduced integration combined with a scaled boundary parametrization. To this end, a Taylor series expansion of the constitutive quantities with respect to the sectional center is carried out, enabling analytical integration of the weak form and reducing the need for integration points to only one per section. The accuracy of the proposed formulation is shown by several numerical examples, including a non-linear patch test. Different loading, e.g. compression under large deformations, and material conditions, such as hyperelastic anisotropy and elasto-plasticity, are considered. The biquadratic serendipity finite element formulation (Q2) and the low-order finite element formulation with hourglass stabilization (Q1STc+) are used for comparison. While the patch test was not fulfilled using higher order shape functions, the formulation led to good results and was able to capture the structure's response accurately. Furthermore, the formulation performed better when the physical element resembled the pre-assigned parent elements. The example of the asymmetrically notched specimen under elasto-plastic material behavior showed that the proposed formulation is able to capture inelasticities.

翻译：本文提出一种基于降阶积分与缩放边界参数化相结合的虚拟单元法(VEM)替代稳定化技术。为此，对截面中心处的本构量进行泰勒级数展开，实现了弱形式的解析积分，并将每个截面所需的积分点数量减少至仅一个。通过含非线性分片试验在内的多个数值算例，验证了所提出公式的精度。研究考虑了不同加载条件（如大变形压缩）与材料特性（包括超弹性各向异性与弹塑性）。采用双二次Serendipity有限单元公式(Q2)与带沙漏稳定化的低阶有限单元公式(Q1STc+)进行对比。尽管使用高阶形函数时无法满足分片试验要求，该公式仍能获得良好结果并准确表征结构响应。此外，当物理单元形态接近预设的母单元时，该公式展现出更优性能。弹塑性材料行为下的非对称缺口试样算例表明，所提公式能够有效捕捉非弹性响应特征。