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首页> 外文期刊>Earthquake Engineering & Structural Dynamics >A Taylor basis for kinematic nonlinear real-time simulations. Part II: The Taylor basis
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A Taylor basis for kinematic nonlinear real-time simulations. Part II: The Taylor basis

机译：用于运动非线性实时模拟的泰勒基础。第二部分：泰勒基础

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摘要

Real-time simulations are used to a significant extent in many engineering fields. However, if nonlinearities are included, the real-time requirement significantly limits the size and complexity of numerical models. The present work constitutes the second of two papers where a general basis method to simulate kinematic nonlinear structures more efficiently is introduced. The advantage of the basis formulation is that it enables the number of basis vectors to be increased without increasing the number of unknown basis co-ordinates. This allows for larger numerical kinematically nonlinear models to run in real time. The basis is organized from a Taylor series that includes the system mode shapes and their complete first-order modal derivatives derived in Part I. The Taylor series predicts fixed linear relations between the modal co-ordinates of the system mode shapes and the modal derivatives, respectively. Thus, the full solution is known solely by determining the modal co-ordinates of the mode shapes, which significantly minimizes the computational costs. Furthermore, it is illustrated that the stability of the Taylor basis formulation is dependent on the mode shape frequencies only, allowing the applied time steps to be significantly larger than in standard nonlinear basis analysis. An example illustrates a case where the computational time can be decreased by one order of magnitude using a Taylor basis formulation compared with a standard basis formulation including identical basis vectors.
机译：实时仿真在许多工程领域中使用了很大程度。但是，如果包括非线性，则实时需求显着限制了数值模型的大小和复杂性。本作者构成了两种纸张中的第二个，其中引入了一种更有效地模拟运动非线性结构的一般基础方法。基础制剂的优点是它使得在不增加未知基础的数量的情况下，它能够增加基础向量的数量。这允许更大的数值运动学非线性模型实时运行。这些基础由泰勒系列组织，包括系统模式形状及其在第一部分中导出的完整的多阶模态衍生物.Taylor系列预测系统模式形状和模态衍生物的模态协调之间的固定线性关系，分别。因此，完整的解决方案仅通过确定模式形状的模态坐标来了解，这显着最小化了计算成本。此外，示出了泰勒基础制剂的稳定性依赖于模式形状频率，允许施加的时间步骤显着大于标准非线性基础分析。一个示例示出了使用泰勒基配制的计算时间可以通过包括相同基载体的标准基础制剂的标准基础制剂的计算时间通过一个幅度减小一个级。

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