求解阶梯连续梁的通用方程

考虑阶形变化截面及不等跨度的情况,建立了求解多跨连续梁变形的通用方程．根据挠曲微分方程并采用奇异函数求解,给出了分析此类连续梁位移的边界参数方程．该参数方程中含有若干待定的初参数和支反力．进一步导出计算变刚度不等跨连续梁位移的递推格式．最后考虑了位移协调条件及平衡条件而得到求解支反力的代数方程组．其计算的实例表明该方法适于编程运算．     

Hestenes' Tetrad and Spin Connections

Defining a spin connection is necessary for formulating Dirac's bispinor equation in a curved space-time. Hestenes has shown that a bispinor field is equivalent to an orthonormal tetrad of vector fields together with a complex scalar field. In this paper, we show that using Hestenes' tetrad for the spin connection in a Riemannian space-time leads to a Yang-Mills formulation of the Dirac Lagrangian in which the bispinor field Ψ is mapped to a set of SL(2,R)× U(1) gauge potentials F_α^K and a complex scalar field ρ. This result was previously proved for a Minkowski space-time using Fierz identities. As an application we derive several different non-Riemannian spin connections found in the literature directly from an arbitrary linear connection acting on the tensor fields (F_α^K, ρ). We also derive spin connections for which Dirac's bispinor equation is form invariant. Previous work has not considered form invariance of the Dirac equation as a criterion for defining a general spin connection.