论文部分内容阅读
有限元法可以计算密度分布、形态复杂物体的重力场垂直分量 g 及重力位二阶导数 W_x■、W_(yy)。取一个包围密度体的足够大的区域,求解 g 的边值问题可表为▽~2g=-4πK(■ρ)/(■y) 在区域内 (■)g)/(■n)+(sin(θ-α))/(r sin θ)g=0 在边界上与上述边值问题相应的变分问题是泛函F(g)=■[(1)/(2)(▽g)~2+4πK(■g)/(■y)ρ]dS+■_Γ(1)/(2)(sin(θ-α))/(r sin θ)g~2dl取极值。用有限元解上述变分问题时,将区域Ω剖分为三角单元,在单元 e 内进行二次函数插值。首先计算各单元的 F_e(g),然后相加组成总体的 F(g),它是各节点待求的 g 的函数。对 F(g)求极值,得一线性代数方程组。解方程组可得各节点的 g。对 g 进行微商,即可得重力位二阶导数。
The finite element method can calculate the density distribution, the vertical component g of gravitational field and the second derivative W_x ■, W_ (yy) of the gravitational field with complex shape. Taking a sufficiently large area around the density body, the problem of solving the boundary value of g can be expressed as ∇ ~ 2g = -4πK (■ ρ) / (■ y) in the area g) / (■ n) + The variational problem corresponding to the above boundary value problem at the boundary is F (g) = ■ [(1) / (2) (∇g) ~ 2 + 4πK (■ g) / (■ y) ρ] dS + ■ _Γ (1) / (2) (sin (θ-α)) / (r sin θ) g ~ 2dl. When finite element method is used to solve the above variational problem, the area Ω is divided into triangular units and quadratic function interpolation is performed in unit e. First calculate F_e (g) for each cell and then add F (g) that makes up the population as a function of g to be sought by each node. Find the extreme value of F (g) to obtain a linear algebraic system. Solution of equations available for each node g. Derivative of g, you can get the second derivative of gravity.