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Nonlinear Bending and Vibration of Beams
Published in Muthukrishnan Sathyamoorthy, Nonlinear Analysis of Structures, 2017
The study of the bending, buckling, and free vibration of straight beams, flat plates, and thin shells forms an important and essential part of the study of the broad field of structural mechanics. All structures deform when subjected to load(s). The load may be static, dynamic, thermal, aeroelastic or hydroelastic, and so on. In the case of a reentry vehicle, for example, it is subjected to thermal and aerodynamic loads. On entering the atmosphere, the reentry vehicle encounters extremely high temperatures while the inside temperature has to be kept at a comfortable 350 or so. Therefore, the stress analysis and design of the heat shield is a challenging problem. An aircraft or missile in flight may encounter gust loads which are dynamic in nature. A beam or column of a building is subjected primarily to static type of loads. In all these cases, the basic problem of structural mechanics is the determination of the deformational response of the structure subjected to loads. This response may involve the determination of the stresses, strains, and displacements at every point of the structure or it may involve the determination of the load(s) when the structure (for example, a wing of an aircraft) can become unstable, as in the case of “wing divergence,” which is a static instability phenomenon. It may also involve dynamic behavior of the structure, particularly the dynamic instability which for an aircraft wing is known as “flutter.”
Convergence deformation monitoring of a shield tunnel based on flexible long-gauge FBG sensors
Published in Mechanics of Advanced Materials and Structures, 2022
Tao Wang, Yongsheng Tang, Hao Yang, Xiangyang Xu, Wei Liu, Xizhi Li
For Part I, according to classic structural mechanics, the deformation caused by stress can be calculated by Eq. (1), in which the structure is divided into many elements. In this part, much of the convergence deformation is caused by bending deformation such that the latter two terms can be omitted. In the equation, is the average bending strain of the it element, is the average axial strain of the ith element, and is the average shear strain of the ith element. is the average virtual bending moment of the ith element. is the average virtual axial force of the ith element. is the average shear force of the ith element. is the length of the ith element. is the element number. is the distance from the sensor location to the neutral axis.
FEM analysis of the stiffness evolution in clustered composites and nanocomposites
Published in Mechanics of Advanced Materials and Structures, 2022
In order to model the mechanical properties of clustered composites and nanocomposites, the finite element (FE) solutions were obtained by using the Comsol Multiphysics software (version 3.5, Comsol AB, Sweden). The problem is solved by means of the 3D structural mechanics module, solid stress strain. The boundary conditions used for calculating the whole stiffens matrix of the nanocomposite are the same as those used in our previous work [18]. Basically, normal or shear stress is applied along six different directions. Stress-free conditions are applied on the external boundaries of the domain, which are not subjected to load. This approach allows for calculating the longitudinal and transversal modulus, as well as the shear modulus and Poisson’s ratio, and the I- and II-order coefficients of mutual influence, as defined by Jones in [32].
Research on shock resistance of shipborne equipment based on multibody system discrete-time transfer matrix method
Published in Ships and Offshore Structures, 2021
Wenqi Zhang, Xiongliang Yao, Zhikai Wang, Yinan Wang
Marine power equipment is a very complex mechanical system, including connecting rod mechanism, gear mechanism, etc. (Yu and Hongxing 2005). The impact dynamics problem of the mechanism is different from that of the structure. Each component can move with each other, and there must be a gap in the connection part. The existence of the gap will lead to the collision between components and the change of boundary. The so-called mechanism can also be called multi-body system. With the development of engineering technology, experts and scholars at home and abroad have made unremitting efforts to put forward and improve various multi-body system dynamics methods, such as the Wittenburg method (Wittenburg and Likins 1978), Schiehlen method (Schiehlen and Werner 1990), Kane method (Kane et al. 1983), etc. These methods promote the development of modern engineering technology, and provide a variety of effective calculation methods for solving mechanical system dynamics problems (Shabana 2013). With the development of finite element and boundary element theory, structural analysis has been programmed and powerful tools have been provided for solving complex structural mechanics problems. Large computer software such as SAP, NASTRAN and ANSYS have been developed.