Mechanical responses of high-performance concrete beam reinforced with CFRP/GFRP tendons based on nonlinear shell beam mixed element

For high-performance concrete (HPC) beams reinforced with hybrid Carbon Fiber Reinforced Polymer/Glass Fiber Reinforced Polymer (CFRP/GFRP) tendons, the nonlinear shell beam mixed element is studied and the whole mechanical process is analyzed. The CFRP/CFRP tendons are simulated with spatial beam element and the HPC beam is modeled with the layered shell element. With the coordination of nodal linear displacement and rotational displacement of CFRP/GFRP tendons element, the contribution of CFRP/GFRP element to stiffness matrix of nonlinear shell beam mixed element is deduced. Then, Jiang’s yielding criterion, Hinton’s crushing criterion, and so on, are used to describe the material nonlinearity of concrete. The new kind of nonlinear shell beam mixed element is achieved and the three-dimensional nonlinear calculation program is developed. The calculative results are consistent with the development trend of test results, which shows the correctness of the nonlinear shell beam mixed element and the reliability of the development program. The mixed element can accurately simulate the geometric configuration of CFRP tendons and realize the tension-compression-bending-shearing performance of CFRP tendons, which is helpful to fully reflect the reinforcement effect of reinforcement in the structure. The computational stiffness is defined and the stiffness degradation experiences three change processes. During the whole processes in the proposed typical load cases, the CFRP/GFRP tendons are still kept in the elastic stages.

Nonlinear Thermo-Electro-Mechanical Vibration of Functionally Graded Piezoelectric Nanoshells on Winkler–Pasternak Foundations Via Nonlocal Donnell’s Nonlinear Shell Theory

The thermo-electro-mechanical nonlinear vibration of circular cylindrical nanoshells on the Winkler–Pasternak foundation is investigated. The nanoshell is made of functionally graded piezoelectric material (FGPM), which is simulated by the nonlocal elasticity theory and Donnell’s nonlinear shell theory. The Hamilton’s principle is employed to derive the nonlinear governing equations and corresponding boundary conditions. Then, the Galerkin’s method is used to obtain the nonlinear Duffing equation, to which an approximate analytical solution is obtained by the multiple scales method. The results reveal that the system exhibits hardening-spring behavior. External applied voltage and temperature change have significant effect on the nonlinear vibration of the FGPM nanoshells. Moreover, the effect of power-law index on the nonlinear vibration of the FGPM nanoshells depends on parameters such as the external applied voltage, temperature change and properties of the Winkler–Pasternak foundation.