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本文采用双5次 B 样条函数作为离散型最小二乘法的试函数,计算和分析了薄板的弯曲问题。所采用的双5次 B 样条的两个一维基事先不满足薄板弯曲平衡微分方程和定解条件中的自由边界条件,但满足固定边的边界条件,稍加处理又可满足简支边的边界条件。这样,对于有着简支边和固定边的各种薄板,只需在板的内部区域建立残数方程,进行简便地计算。采用本法,计算结果的误差较小,计算机程序设计简单,编制容易,计算工作量少。
In this paper, a double-fifth-order B-spline function is used as a trial function of the discrete least-squares method to calculate and analyze the bending problem of thin plates. The two one-dimensional B-spline two-dimensional BMIs do not satisfy the free-form boundary conditions for the plate bending equilibrium differential equations and the solution conditions, but satisfy the boundary conditions of the fixed edges. condition. In this way, for all kinds of thin plates with simple edges and fixed edges, the residual equation need only be established in the inner area of the plate for easy calculation. With this method, the error of the calculation result is small, the computer program design is simple, the preparation is easy, and the calculation workload is small.