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以三次B样条作为插值函数,用变分原理求解工程中常用的规则区域连续体的样条有限元法,比通常有限元法具有精度高、计算量少、程序简单等显著特点,受到计算数学、计算力学以及工程界的重视。样条有限元法在解算任何具体问题时,都可以采取形成总刚度矩阵方程[k]{c}={v}来统一处理。其中,荷载矩阵{v}的确定是重要的环节。本文对各种边界条件下各种荷载矩阵进行了研究,并给出了显式表达式,可以避免形成荷载矩阵时的Kronecker乘积运算,大大地节省了计算机的内存和运算,进一步发挥了样条有限元法的特点,使中、小型电算机有可能进行位移、内力分析。
Using cubic B-spline as an interpolation function, the variational principle is used to solve the spline finite element method of the regular region continuum commonly used in the engineering. Compared with the ordinary finite element method, the finite element method has the characteristics of high precision, low computational complexity, simple procedure and other significant features. Mathematics, computational mechanics, and the engineering community pay attention to it. When the spline finite element method solves any specific problem, it can be formed by forming the total stiffness matrix equation [k]{c}={v}. Among them, the determination of the load matrix {v} is an important link. In this paper, various load matrices under various boundary conditions are studied, and explicit expressions are given. This can avoid the Kronecker product operation when forming the load matrix, which greatly saves the memory and operation of the computer, and further develops the spline. The characteristics of the finite element method make it possible for small and medium-sized computers to analyze displacement and internal forces.