Shell elements are extensively used by engineers for modeling the behavior of shell structures. Among common shell elements, triangular shell elements are not influenced by element warping. This paper proposes a new three-node triangular flat shell element with six degrees of freedom per each node, named TMRFS. The element is formed by assemblage of new bending and membrane elements. The bending element is formulated based on the hybrid displacement function element method and Mindlin–Reissner plate theory. In this element, an assumed displacement function is employed as the trial function. The membrane component is an unsymmetric triangular membrane element with drilling vertex rotations. The membrane element employs two different types of displacement fields as the test and trial functions. The test function is a displacement field which is the same as one used in well-known Allman triangular element. Meanwhile, instead of displacement field, the analytical stress field is considered as the trial function. Numerical tests show that the accuracy of the proposed flat shell element is reasonable in comparison with some popular triangular elements and its performance is insensitive to geometry, load and boundary conditions. Moreover, the proposed element preserves the advantages of its formulation including free of membrane locking, shear locking and stiffness matrix singularity problems.

壳元被工程师广泛用于对壳结构的行为进行建模。在常见的壳单元中，三角形壳单元不受单元翘曲的影响。本文提出了一个新的三节点三角形扁平壳单元，每个节点具有六个自由度，称为TMRFS。该元件是通过组装新的弯曲元件和薄膜元件而形成的。弯曲单元是根据混合位移函数单元法和Mindlin-Reissner板理论来制定的。在这个元素中，假定的位移函数被用作试验函数。膜组件是具有钻孔顶点旋转的不对称三角形膜单元。膜元件采用两种不同类型的位移场作为测试和试验功能。测试函数是一个位移场，它与众所周知的Allman三角单元中使用的场相同。同时，代替位移场，将分析应力场视为试验函数。数值测试表明，与一些流行的三角形单元相比，所提出的扁平壳单元的精度是合理的，并且其性能对几何形状，载荷和边界条件不敏感。而且，所提出的元件保留了其配方的优点，包括没有膜锁定，剪切锁定和刚度矩阵奇异性问题。数值测试表明，与一些流行的三角形单元相比，所提出的扁平壳单元的精度是合理的，并且其性能对几何形状，载荷和边界条件不敏感。而且，所提出的元件保留了其配方的优点，包括没有膜锁定，剪切锁定和刚度矩阵奇异性问题。数值测试表明，与一些流行的三角形单元相比，所提出的扁平壳单元的精度是合理的，并且其性能对几何形状，载荷和边界条件不敏感。而且，所提出的元件保留了其配方的优点，包括没有膜锁定，剪切锁定和刚度矩阵奇异性问题。