考虑预应力作用的索杆张力结构冗余度分析

Redundancy Investigation of Pre-Tensioning Cable-Strut Systems Considering the Effect of Pre-Stresses

在考虑预应力作用的前提下,给出了由弹性冗余度和几何冗余度组成的索杆张力结构体系的冗余度定义;基于能量理论提出了统一的冗余度计算方法,其中采用更新的拉格朗日格式建立了一个关于位移增量的非线性应变能表达式;在求解过程中对应变能表达式进行线性化处理,并根据势能驻值原理推导了冗余度计算公式,以用于施加预应力后的索杆张力结构体系分析.结果表明,与以往的冗余度计算方法相比,所提出的方法给出了显式几何冗余度计算公式,阐明了弹性冗余度和几何冗余度的物理意义,可用于预张力作用的索杆张力结构体系分析.

A unified redundancy formulation for both the elastic redundancy and the geometrical redundancy is proposed to be applicable for cable-strut systems at pre-stressed state by considering the effect of pre- stresses. The updated Lagrange formulation is used to establish a nonlinear description of strain energy with respect to the displacement increment; a common linearization method is then adopted to reduce the numerical complexity. Based on this reasonable simplification, a unified evaluation for the redundancy is derived by using the principle of minimum potential energy, which is interpreted as a useful method for system identification at pre-stressed configuration. In comparison with existing studies, an explicit formula of geometrical redundancy is firstly presented and the physical meanings of redundancy are clearly ad dressed. Furthermore, it can be concluded that this proposed evaluation is valid for cable-strut systems with introduced pre-tensions.