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通过基于完整位移模式与基于常规位移模式伽辽金方程的比较,导出了伽辽金方程精确成立的条件。论证了位移模式与泡函数的相关性。提出了一次元与泡函数结合的单元方案。利用精确成立的条件,通过量级分析,保留泡函数主要的影响项,避免了求解泡函数的解析表达式。该文的结果达到了h4阶的收敛精度,与收敛精度为h2阶的常规一次元相比,计算量并没有本质上的增加。理论分析和数值计算表明,该文单元是一个比高次元性能优的单元。
Through the comparison of the Galerkin equation based on the complete displacement mode and the conventional displacement mode, the conditions for the exact establishment of the Galerkin equation are derived. The correlation between displacement mode and bubble function is demonstrated. A unitary scheme combining the element and bubble function is proposed. By using the exact conditions, through the analysis of the order of magnitude, the main influence items of the bubble function are preserved, and the analytical expression for solving the bubble function is avoided. The result of this paper achieves the convergence accuracy of h4 order. Compared with the conventional one-dimensional element with h2 order of convergence, the computational complexity does not increase intrinsically. The theoretical analysis and numerical calculation show that the unit is a better unit than the higher-order unit.