Hencky bar-chain model (HBM) is developed for shape optimization of circular arches. HBM is ease to handle minimum cross-sectional area constraint. Analytical optimization solutions are obtained via HBM.
This paper is concerned with the development of the Hencky bar-net model (HBM) for free vibration analyses of rectangular plates with mixed boundary conditions and point supports. The HBM is a two-dimensional discrete net system composed of rigid segments connected by frictionless hinges and rotational springs. In the model, bending is accommodated by rotational springs at each joint while the twisting by a diagonal spring system in each grid cell. The total mass of the plate is distributed as lumped mass at each joint and the continuous boundary stiffness of plate is simulated by springs located at the edge joints. Owing to the discrete property of HBM, it is able to readily handle any boundary conditions of plates including mixed boundary conditions and point supports. The HBM is herein used to solve some vibration problems of rectangular plates with mixed boundary conditions and point supports to demonstrate its accuracy and convenience for plate analyses.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.