Convex Polygonal Finite Macroelements: Closed-Form Kinematics and Exact Quadrature

凸多边形宏元 摘要 该建议的目的是开发有限宏单元没有任何限制的边界顶点的数量。 为了达到尽可能高的精度，研究量化的形状和大小的空间变化率与最小的离散化。 计算机代数程序将构造二维凸多边形的形状函数。 有理多项式Pade插值的解析微分将产生大的应变张量。 封闭形式的积分将导致质量和刚度的性质。 形态计算与分母多项式的五十二度产生了令人鼓舞的数值结果。 嗅觉区附近的神经颅骨的宏量元素生长模型将被维斯相对于解剖学的功能矩阵理论。 生长分布的就绪轮廓图将从临床观察到的生物对象的边界轮廓生成，头骨，大脑，心脏和眼睛，用于医学诊断

CONVEX POLYGONAL FINITE MACROELEMENTS Abstract The proposal aims at developing finite macroelements without any restriction on the number of boundary vertices. To achieve the highest possible accuracy, the research quantities the spatial rate of change in shape and size with minimal discretization. Computer algebra programs will construct shape functions for two-dimensional convex polygons. Analytical differentiation of the rational polynomial Pade interpolants will yield large strain tensors. Closed form integration will lead to mass and stiffness natrices. Morphometric computation with denominator polynomials of fifty two degrees yielded encouraging numerical results. The macroelement growth model of the neuro-skull neighboring the olfactory region will be examined vis a vis the functional matrix theory of anatomy. Ready contour plots of growth distribution will be generated from clinically observed boundary profiles of biological objects e.., skulls, brains, hearts and eyes, for medical diagnosis.