Perumal Logah, Koh Wei Hao
Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450 Melaka, Malaysia.
MethodsX. 2023 Jan 24;10:102027. doi: 10.1016/j.mex.2023.102027. eCollection 2023.
Finite elements are often formulated by imposing sufficient conditions to ensure convergence and good accuracy. This work demonstrates a new technique to impose compatibility and equilibrium conditions for membrane finite elements that are formulated based on the strain approach.•The compatibility and equilibrium conditions are imposed onto the initial formulations (or test functions) by using corrective coefficients ( , and ).•The technique is found to be capable of producing alternate or similar forms for the test functions. Performances of the resultant (or final) formulations are shown by solving three benchmark problems. Additionally, a new technique to formulate strain-based triangular transition elements (denoted as SB-TTE) is introduced.•The new technique introduces another node (the fourth node) at one of the sides of a strain-based triangular element (mid-node, which is needed for the quadtree-based triangular mesh generation) without adding a degree of freedom.
有限元通常通过施加充分条件来确保收敛性和良好的精度。本文展示了一种为基于应变方法构建的膜有限元施加协调和平衡条件的新技术。
• 通过使用修正系数（ 、 和 ）将协调和平衡条件施加到初始公式（或测试函数）上。
• 发现该技术能够为测试函数生成替代形式或相似形式。通过求解三个基准问题展示了所得（或最终）公式的性能。此外，还介绍了一种构建基于应变的三角形过渡单元（记为SB-TTE）的新技术。
• 该新技术在基于应变的三角形单元的一条边上引入另一个节点（第四个节点）（中间节点，这是基于四叉树的三角形网格生成所需要的），而不增加自由度。
