Development of New Analytical Techniques for Randomly Nonlinear Structural Systems

[9531719]林工程结构经常受到动态随机激励，这些激励只能用概率和统计来描述。这种激励的例子包括地震地面加速度、湍流风、海浪和交通负荷。人们也很清楚地认识到，大多数建筑不需要或不应该为永生而设计；否则，所需的尺寸可能太大而不实用，或者成本太高。因此，在设计时必须考虑大变形和破坏的可能性。然后，必须在结构系统的预期最小使用寿命内选择最佳总成本，包括初始建造成本、维护和维修成本、与服务中断相关的成本等。大变形随机激励结构的非线性问题是一个很困难的问题，因为必须考虑结构的非线性行为。对于非线性结构，已知的精确解析解在很大程度上仅限于白噪声激励下的单自由度情况。对多自由度情况的推广只有在附加的严格限制条件下才能成功。PI计划开发新的先进分析技术，以获得随机动力激励下多自由度非线性结构系统的响应统计和失效概率。几何非线性和材料非线性都将被考虑。

9531719 Lin Engineering structures are often exposed to dynamic random excitations which can only be described in terms of probability and statistics. Examples of such excitations include seismic ground accelerations, turbulent winds, ocean waves, and traffic loads. It has also been well recognized that most structures need not be or should not be designed for eternal life; otherwise, the required size may be too large to be practical, or the cost too high. Thus the possibility of large deformation and failure must be considered in the design. The choice must then be made for the optimal total cost within a desired minimum service life of a structural system, including the costs of initial construction, maintenance and repair, costs associated with interruption of service, etc. The problem of a randomly excited structures undergoing large deformation is a difficult one, since nonlinear behaviors of the structure must be taken into account. For nonlinear structures, known exact analytical solutions are, by an large restricted to the case of single degree of freedom under white noise excitations. Extension to the case of multiple degrees of freedom is successful only under additional severe restrictions. The PI plans to develop new advanced analytical techniques to obtain the response statistics and probability of failure for multi-degree-of-freedom nonlinear structural systems under random dynamical excitations. Both geometrical and material nonlinearities will be considered.