Abstract This paper presents a new force method to predict the structural response of statically and kinematically indeterminate systems that can be stabilized through prestress, i.e. prestress-stable structures. This new force method, here named Extended Integrated Force Method (IFME), extends the existing Integrated Force Method (IFM) which is only applicable to the analysis of kinematically determinate systems. The product force concept is adopted and incorporated into the IFME to model the effect of infinitesimal mechanisms. This makes the IFME capable of dealing with cases in which the external loads contain components that cannot be taken by the system in its initial configuration. As the original IFM, the IFME bypasses the well-known concept of redundant forces and basis determinant structure of the Standard Force Method (SFM) by taking the internal forces as the independent variables which are obtained simultaneously. A proof is provided to show that, when the product force is not included in the formulation, the IFME reduces to the IFM for kinematically determinate systems and it also reduces to another force method based on singular value decomposition of the equilibrium matrix which is here named SVD-FM. Compared to the better known Displacement Method (DM), the IFME is a suitable alternative and it offers a deeper insight into the structure response which is decoupled into an extensional and an inextensional part for prestress-stable kinematically indeterminate systems. Numerical examples are carried out to test accuracy and effectiveness of the IFME on kinematically indeterminate structures with multiple self-stress states and mechanism modes. Application of the IFME to active structural control of kinematically indeterminate systems is also discussed through a numerical example.

中文翻译：

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用于分析预应力稳定静态和运动学不确定结构的扩展综合力法

摘要 本文提出了一种新的力方法来预测静态和运动学不确定系统的结构响应，这些系统可以通过预应力稳定，即预应力稳定结构。这种新的力方法，这里称为扩展综合力法 (IFME)，扩展了现有的综合力法 (IFM)，后者仅适用于运动学确定系统的分析。产品力概念被采用并纳入 IFME 以模拟无穷小的机制的影响。这使得 IFME 能够处理外部负载包含系统在其初始配置中无法承受的组件的情况。作为最初的 IFM，IFME 通过将内力作为同时获得的自变量，绕过了众所周知的冗余力概念和标准力法 (SFM) 的基础行列式结构。提供了一个证明来证明，当公式中不包含乘积力时，IFME 简化为运动学确定系统的 IFM，它还简化为另一种基于平衡矩阵奇异值分解的力方法，此处称为SVD-FM。与众所周知的位移法 (DM) 相比，IFME 是一种合适的替代方法，它提供了对结构响应的更深入了解，该结构响应被解耦为预应力稳定运动学不确定系统的拉伸和非拉伸部分。数值例子用于测试IFME在具有多种自应力状态和机制模式的运动学不确定结构上的准确性和有效性。还通过数值例子讨论了 IFME 在运动学不定系统的主动结构控制中的应用。