Through a critical review of the various component mode synthesis techniques developed in the past, it is shown that both Craig–Bampton’s and Herting’s methods are particular cases of the mode-acceleration method and furthermore, Rubin’s method is equivalent to Herting’s method. Consequently, the mode-acceleration method is the approach of choice due to its simplicity and because unlike the other methods, it imposes no restriction on the selection of the modes. Next, a general approach to the modal reduction of geometrically nonlinear structures is developed within the framework of the motion formalism, based on the small deformation assumption. The floating frame of reference is defined unequivocally by imposing six linear constraints on the deformation measures, which are defined as the vectorial parameterization of the relative motion tensor that brings the fictitious rigid-body configuration to its deformed counterpart. This approach yields deformation measures that are both objective and tensorial, unlike their classical counterparts that share the first property only. Derivatives are expressed in the material frame, leading to computationally advantageous properties: tangent matrices are functions of the deformation measures only and become nearly constant during the simulation. Numerical examples demonstrate the accuracy, robustness, and numerical efficiency of the proposed approach. With a small number of modal elements, the formulation is able to capture geometrically nonlinear effects accurately, even in the presence of inherently nonlinear phenomena such as buckling.

通过对过去开发的各种成分模式合成技术的严格审查，可以看出Craig–Bampton方法和Herting方法都是模式加速方法的特例，此外，Rubin方法等效于Herting方法。因此，模式加速方法由于其简单性而成为选择的方法，并且因为与其他方法不同，它对模式的选择没有任何限制。接下来，基于小变形假设，在运动形式主义的框架内开发了一种几何非线性结构的模态简化的通用方法。通过在变形量度上施加六个线性约束来明确定义浮动参考系，定义为相对运动张量的矢量参数化，它将虚拟的刚体构造带到变形的对应部分。这种方法产生的变形量度既是客观的又是张量的，这不同于仅具有第一特性的经典变形量度。导数在材料框架中表示，从而具有计算上的优势：切线矩阵仅是变形量度的函数，并且在模拟过程中几乎变为常数。数值算例表明了该方法的准确性，鲁棒性和数值效率。使用少量的模态元素，即使在存在诸如屈曲之类的固有非线性现象的情况下，该公式也能够准确地捕获几何非线性效应。