CONTACT PROBLEM FOR ORTHOTROPIC PLATES OF VARIABLE THICKNESS WITH A SPATIALLY INHOMOGENEOUS BASE

2021 ◽  
pp. 90-99
Author(s):  
Н. Н. Некрасова
Keyword(s):  
Variable Thickness ◽  
Finite Difference Methods ◽  
Variable Stiffness ◽  
Spatial Problem ◽  
Orthotropic Plates ◽  
Soil Thickness ◽  
Elastic Foundations ◽  
Calculation Technique ◽  
Spatially Inhomogeneous ◽  
Rectangular Slab

В работе приведено численное моделирование пространственной задачи контактного взаимодействия ортотропных плит переменной жесткости с упругими основаниями. Используемая методика расчета пригодна в случае любых известных контактных моделей упругих оснований. В качестве примера приведены численные результаты для пространственно-неоднородных оснований типа упругих слоев постоянной и переменной толщины. Система интегро-дифференциальных уравнений, к которой сводится задача, решается численно, сочетанием методов конечных разностей типа сквозного счета и граничных элементов. Найдены прогибы, изгибающие моменты и распределения контактных давлений прямоугольной плиты переменной жесткости, полностью примыкающей к основанию. Приводится анализ влияния на напряженно-деформированное состояние плиты, изменения ортотропных свойств ее материала и степень неравномерной сжимаемости толщи грунта. Разработанная методика позволяет эффективно моделировать работу плитных фундаментных конструкций, когда необходим учет неоднородности грунтов сжимаемой толщи в пределах габарита зданий или сооружений. The paper presents a numerical simulation of the spatial problem of contact interaction of orthotropic slabs of variable stiffness with elastic foundations. The calculation technique used is suitable for any known contact models of elastic foundations. As an example, numerical results are given for spatially inhomogeneous foundations such as elastic layers of constant and variable thickness. The system of integrodifferential equations, to which the problem is reduced, is solved numerically by a combination of finite difference methods such as end-to-end counting and boundary elements. Deflections, bending moments and contact pressure distributions of a rectangular slab of variable stiffness, completely adjacent to the base, are found. An analysis of the influence on the stress-strain state of the slab of changes in the orthotropic properties of its material and the degree of uneven compressibility of the soil thickness is given. The developed technique makes it possible to effectively simulate the operation of slab foundation structures when it is necessary to take into account the heterogeneity of the soil of the compressible strata within the dimensions of buildings or structures.

Vibration of Orthotropic Rectangular Plates With Variable Thickness

1989 ◽  
Vol 111 (1) ◽  
pp. 101-103 ◽  
Author(s):  
Wei-Cheun Liu ◽  
Stanley S. H. Chen
Keyword(s):  
Boundary Conditions ◽  
Computer Program ◽  
Variable Thickness ◽  
Energy Method ◽  
Natural Frequencies ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Orthotropic Properties

The problem vibration of rectangular orthotropic plates with variable thickness and mixed boundary conditions are solved by a modified energy method. A general expression is written for the deflection of the plate without aiming at any particular combination of boundary conditions. Boundary conditions are satisfied approximately by adjusting a set of so-called fixity factors. A computer program has been developed to solve for natural frequencies of plates with variable thicknesses and having different orthotropic properties.

LINEAR BENDING ANALYSIS OF INHOMOGENEOUS VARIABLE-THICKNESS ORTHOTROPIC PLATES UNDER VARIOUS BOUNDARY CONDITIONS

2007 ◽  
Vol 04 (03) ◽  
pp. 417-438 ◽  
Author(s):  
A. M. ZENKOUR ◽  
M. N. M. ALLAM ◽  
D. S. MASHAT
Keyword(s):  
Boundary Conditions ◽  
Variable Thickness ◽  
Flexural Rigidity ◽  
Approximate Solutions ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Thickness Parameter ◽  
Space Concept

An exact solution to the bending of variable-thickness orthotropic plates is developed for a variety of boundary conditions. The procedure, based on a Lévy-type solution considered in conjunction with the state-space concept, is applicable to inhomogeneous variable-thickness rectangular plates with two opposite edges simply supported. The remaining ones are subjected to a combination of clamped, simply supported, and free boundary conditions, and between these two edges the plate may have varying thickness. The procedure is valuable in view of the fact that tables of deflections and stresses cannot be presented for inhomogeneous variable-thickness plates as for isotropic homogeneous plates even for commonly encountered loads because the results depend on the inhomogeneity coefficient and the orthotropic material properties instead of a single flexural rigidity. Benchmark numerical results, useful for the validation or otherwise of approximate solutions, are tabulated. The influences of the degree of inhomogeneity, aspect ratio, thickness parameter, and the degree of nonuniformity on the deflections and stresses are investigated.

THE NON-CLASSICAL PROBLEM OF AN ELASTICALLY CLAMPED ORTHOTROPIC BEAM OF VARIABLE THICKNESS UNDER THE COMBINED ACTION OF COMPRESSIVE FORCES AND TRANSVERSE LOAD

2018 ◽  
Vol 52 (2 (246)) ◽  
pp. 101-108
Author(s):  
R.M. Kirakosyan ◽  
S.P. Stepanyan
Keyword(s):  
Variable Thickness ◽  
Classical Problem ◽  
Compressive Force ◽  
Transverse Load ◽  
Simultaneous Action ◽  
Refined Theory ◽  
Orthotropic Plates ◽  
Combined Action ◽  
Beam Bending ◽  
The Stability

On the basis of the refined theory of orthotropic plates of variable thickness, the equations of the beam bending problem are obtained with the simultaneous action of compressive forces and transverse load. It is accepted that the edges of the beam have an elastically clamped support and the reduction of the compressive force by the support due to friction is taking into account. Passing to dimensionless quantities, a certain problem is solved. The stability of a beam is discussed. Based on the results obtained, conclusions are drawn.

Bimodal Optimization of Compressed Columns on Elastic Foundations

1986 ◽  
Vol 53 (1) ◽  
pp. 130-134 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson ◽  
N. Olhoff
Keyword(s):  
Optimal Design ◽  
Cross Sections ◽  
Variable Thickness ◽  
Buckling Load ◽  
Optimal Designs ◽  
Constant Thickness ◽  
Buckling Modes ◽  
Elastic Foundations ◽  
Bimodal Optimization ◽  
Lightweight Core

We consider columns attached to elastic foundations and compressed by axial end loads. Pinned-pinned, clamped-clamped, and pinned-clamped boundary conditions are treated. The columns have rectangular sandwich cross sections with a fixed lightweight core and identical face sheets of variable thickness. For given total volume, we optimize the variation of the thickness along the column so as to maximize the buckling load. In most cases, the optimal design is bimodal (i.e., associated with two buckling modes). The optimal designs depend on the foundation stiffness, and the largest increase in buckling load relative to a column with constant thickness is 22 percent.

Buckling of Axisymmetric Cylindrical Shells of Variable Thickness: Finite Difference Solution

2007 ◽  
Author(s):  
Gurinder Singh Brar ◽  
Yogeshwar Hari ◽  
Dennis K. Williams
Keyword(s):  
Cylindrical Shell ◽  
Finite Difference ◽  
Variable Thickness ◽  
Cylindrical Shells ◽  
Finite Difference Methods ◽  
Large Diameter ◽  
Buckling Load ◽  
Thin Wall ◽  
Shells Of Revolution ◽  
Equilibrium Equations

This paper presents the third of a series of solutions to the buckling of imperfect cylindrical shells subjected to an axial compressive load. In particular, the initial problem reviewed is the case of a homogeneous cylindrical shell of variable thickness that is of an axisymmetric nature. The equilibrium equations as first introduced by Donnell over seventy years ago are discussed and reviewed in establishing a basis for embarking upon a solution that utilizes finite difference methods to solve the resulting equilibrium and compatibility equations. The ultimate objective of these calculations is to achieve a quantitative assessment of the critical buckling load considering the small axisymmetric deviations from the nominal cylindrical shell wall thickness. Clearly in practice, large diameter, thin wall shells of revolution that form stacks are never fabricated with constant diameters and thicknesses over the entire length of the assembly. The method and results described herein are in stark contrast to the “knockdown factor” approach currently utilized in ASME Code Case 2286-1. The results obtained by finite difference method agree well with those published by Elishakoff and Williams for the prediction of buckling load.

scholarly journals To Calculation of Rectangular Plates on Periodic Oscillations

2018 ◽  
Vol 245 ◽  
pp. 01003 ◽  
Author(s):  
Rustamkhan Abdikarimov ◽  
Dadakhan Khodzhaev ◽  
Nikolay Vatin
Keyword(s):  
Variable Thickness ◽  
Dynamic Instability ◽  
Rheological Parameters ◽  
Problem Solution ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Weakly Singular Kernel ◽  
Parametric Oscillations ◽  
Plate Of Variable Thickness ◽  
Plates Of Variable Thickness

Geometrically nonlinear mathematical model of the problem of parametric oscillations of a viscoelastic orthotropic plate of variable thickness is developed using the classical Kirchhoff-Love hypothesis. The technique of the nonlinear problem solution by applying the Bubnov-Galerkin method at polynomial approximation of displacements (and deflection) and a numerical method that uses quadrature formula are proposed. The Koltunov-Rzhanitsyn kernel with three different rheological parameters is chosen as a weakly singular kernel. Parametric oscillations of viscoelastic orthotropic plates of variable thickness under the effect of an external load are investigated. The effect on the domain of dynamic instability of geometric nonlinearity, viscoelastic properties of material, as well as other physical-mechanical and geometric parameters and factors are taken into account. The results obtained are in good agreement with the results and data of other authors.

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