The dynamic response of a cable-stayed bridge that consists of a simply supported four-cable-stayed deck beam and two rigid towers, subjected to a distributed vortex shedding force on the deck beam with a uniform rectangular cross section, is studied in this work. The cable-stayed bridge is modeled as a continuous system, and the distributed vortex shedding force on the deck beam is modeled using Ehsan-Scanlan’s model. Orthogonality conditions of exact mode shapes of the linearized undamped cable-stayed bridge model are employed to convert coupled governing partial differential equations of the original cable-stayed bridge model with damping to a set of ordinary differential equations by using Galerkin method. The dynamic response of the cable-stayed bridge is calculated using Runge-Kutta-Felhberg method in MATLAB for two cases with and without geometric nonlinear terms. Convergence of the dynamic response from Galerkin method is investigated. Numerical results show that the geometric nonlinearities of stay cables have significant influence on vortex-induced vibration of the cable-stayed bridge. There are different limit cycles in the case of neglecting the geometric nonlinear terms, and there are only one limit cycle and chaotic responses in the case of considering the geometric nonlinear terms.

In this work, an eigenfunction expansion approach is used to study the dynamic response of a cable-stayed bridge excited by a continuous sequence of identical, equally spaced moving forces. The nonlinear dynamic response of the cable-stayed bridge is obtained by simultaneously solving nonlinear and linear partial differential equations that govern transverse and longitudinal vibrations of stay cables and transverse vibrations of segments of the deck beam, respectively, along with their boundary and matching conditions. Orthogonality conditions of exact mode shapes of the linearized cable-stayed bridge model are employed to convert the coupled nonlinear partial differential equations of the original nonlinear model to a set of ordinary differential equations by using the Galerkin method. The dynamic response of the cable-stayed bridge is numerically solved. Convergence of the dynamic response from the Galerkin method is investigated. Effects of close natural frequencies, mode localization, the distance between any two neighboring forces, and geometric nonlinearities of stay cables on the forced dynamic response of the cable-stayed bridge are captured using a convergent modal truncation.

The present study is devoted to extending Barlat’s famous yield criteria to tension–compression asymmetry by a novel method originally introduced by Khan, which can decouple the anisotropy and tension–compression asymmetry characteristics. First, Barlat (1987) isotropic yield criterion, which leads to a good approximation of yield loci calculated by the Taylor–Bishop–Hill crystal plasticity model, is extended to include yielding asymmetry. Furthermore, the famous Barlat (1989) anisotropic yield criterion, which can well describe the plastic behavior of face-centered cubic (FCC) metals, is extended to take the different strength effects into account. The proposed anisotropic yield criterion has a simple mathematical form and has only five parameters when used in planar stress states. Compared with existing theories, the new yield criterion has much fewer parameters, which makes it very convenient for practical applications. Furthermore, all coefficients of the criterion can be determined by explicit expressions. The effectiveness and flexibility of the new yield criterion have been verified by applying to different materials. Results show that the proposed theory can describe the plastic anisotropy and yielding asymmetry of metals well and the transformation onset of the shape memory alloy, showing excellent predictive ability and flexibility.