The article is devoted to the theoretical calculation of the box-shaped structure of large-panel buildings on dynamic effects, taking into account the spatial work of transverse and longitudinal walls under dynamic effects, set by the base displacement according to a sinusoidal law. The problem is solved using the finite difference method.
The paper is devoted to the numerical solution of the problem of transverse oscillations of a multi-storey building within the framework of a continuous plate model under seismic effects. Cantilevers anisotropic plate is proposed as a building dynamic model, the theory of which is developed in the framework of a three-dimensional dynamic theory of elasticity and takes into account not only structural forces and moments but also the bimoments. The proposed plate model of a building allows us to take into account and study all types of different spatial oscillations of the building structure under the impacts different in direction. Formulas are given for the reduced density, elastic moduli, and shear of the plate model of the building. The base acceleration, given in time by a harmonic law, is taken as a seismic impact. The problem is solved by the finite difference method. Examples are considered and numerical results are obtained. Waveform, displacements, and accelerations distribution diagram of multi-storey high-rise buildings under transverse oscillations are plotted.
The paper is devoted to dynamic design of thick orthotropic cantilever plates by applying the bimoment theory of plates, which takes into account the forces, moments and bimoments; and the theory takes into account nonlinear law of displacements distribution in cross section of the plate. The methods for constructing bimoment theory are based on Hooke's Law, three-dimensional equations of the theory of dynamic elasticity and the method of displacements expansion into Maclaurin series. The article gives the expressions to determine the forces, moments and bimoments. Bimoment theory of plates is described by two unrelated two-dimensional systems with nine equations in each. On each edge of the plate, depending on the type of fastening, nine boundary conditions are given. As an example, the solution of the problem of dynamic bending of thick isotropic and orthotropic plate under the influence of transverse dynamic loads in the form of the Heaviside function is given. The equations of motion of the plate are solved by numerical method of finite differences. The numerical results are obtained for isotropic and orthotropic plate. The graphs of changes of displacements and stresses of faces surfaces of the plate are presented. Maximum values of these displacements are found and analyzed. It is shown that by Timoshenko theory numerical values of stresses are much smaller compared to the ones obtained by bimoment theory of plates. Maximum numerical values of generalized displacements, forces, moments, and bimoments are obtained and presented in tabular form. The analysis of numerical results is done and the conclusions are drawn.
Continuum plate model in the form of a cantilever anisotropic plate developed in the framework of the bimoment theory of plates describing seismic oscillations of buildings is proposed in this paper as a dynamic model of a building. Formulas for the reduced moduli of elasticity, shear and density of the plate model of a building are given. Longitudinal oscillations of a building are studied using the continuum plate and box-like models of the building with Finite Element Model. Numerical results are obtained in the form of graphs, followed by their analysis.
A method for dynamic calculation of a box-like structure, consisting of interconnected longitudinal and transverse plate and beam elements is developed. The problem is posed of spatial vibrations of the box-like structure of a building under dynamic impact determined by its base motion according to a sinusoidal law. It is assumed that the external load-bearing walls of the building, perpendicular to the direction of the seismic effect, work on transverse bending only. The interior panels, located in the direction of external impact, are subjected to tension-compression and shear in their planes. Equations of vibrations of the points of panels, box beams, boundary and initial conditions of the problem are given. In the areas of butt joints of panels, full contact conditions are set to ensure the equality of displacements and stresses. Within the framework of the finite difference method, a methodology was developed for dynamic calculation of box-like structures. Numerical results of stresses over time in the hazardous areas of the box were obtained. The laws of changes in the maximum stress values in characteristic sections of the panels are graphically presented as a function of time.
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