scholarly journals Application of Mindlin's theory for analysis of footing plate bending based on experimental research

2010 ◽  
Vol 8 (2) ◽  
pp. 211-223 ◽  
Author(s):  
Biljana Mladenovic ◽  
Zoran Bonic ◽  
Marina Mijalkovic ◽  
Petar Dancevic ◽  
Nebojsa Davidovic
Keyword(s):  
Stress State ◽  
Analytical Solution ◽  
Experimental Research ◽  
Plate Theory ◽  
Material Behavior ◽  
Plate Bending ◽  
First Order ◽  
Basic Equations ◽  
Concrete Footing ◽  
Mindlin’S Theory

The assumptions and basic equations of the first-order shear deformation plate theory of Mindlin, as one which provides more accurate solutions compared to the classical theory, are briefly presented in this paper. Application of one analytical solution derived according to this theory is presented by use of example of stress-state and deformations calculation of the reinforced concrete footing, which has been the object of recent author's experimental research. Numerical results obtained by applied procedure, which refer to the elastic domain of material behavior, are compared with experimentally obtained data of deflections of footing plate midpoint. .

Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field

2021 ◽  
Vol 76 (3) ◽  
pp. 265-283
Author(s):  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Axial Magnetic Field ◽  
Order Approximation ◽  
Ideal Gas ◽  
Field Region ◽  
First Order ◽  
First Order Approximation ◽  
Flow Variables

Abstract The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.

Delamination of Laminate Plates

2014 ◽  
Vol 969 ◽  
pp. 97-100 ◽  
Author(s):  
Eva Kormaníková
Keyword(s):  
Finite Element Analysis ◽  
Mixed Mode ◽  
Plate Theory ◽  
Laminate Plate ◽  
Element Analysis ◽  
Interface Elements ◽  
First Order ◽  
Plate Elements ◽  
Interface Modeling ◽  
Shear Deformable

The paper deals with numerical modeling of delamination of laminate plate consists of unidirectional fiber reinforced layers. The methodology adopts the first-order shear laminate plate theory and fracture and contact mechanics. There are described sublaminate modeling and delamination modeling by the help of finite element analysis. With the interface modeling there is calculated the energy release rate along the lamination front. Numerical results are given for mixed mode delamination problems by implementing the method in a 2D finite analysis, which utilizes shear deformable plate elements and interface elements. Numerical example is done by the commercial ANSYS code.

A Viscoelastic Correspondence Principle for Plane Membranes Subjected to Lateral Pressure

1983 ◽  
Vol 50 (4a) ◽  
pp. 740-742 ◽  
Author(s):  
B. Stora˚kers
Keyword(s):  
Time Dependence ◽  
Viscoelastic Material ◽  
Lateral Pressure ◽  
Correspondence Principle ◽  
Material Model ◽  
Material Behavior ◽  
Linear Elastic Material ◽  
First Order ◽  
Linear Elastic ◽  
Consistent Approximation

The classical Fo¨ppl equations, governing the deflection of plane membranes, constitute the first-order consistent approximation in the case of linear elastic material behavior. It is shown that despite the static and kinematic nonlinearities present, for arbitrary load histories a correspondence principle for viscoelastic material behavior exists if all relevant relaxation moduli are of uniform time dependence. Application of the principle is illustrated by means of a popular material model.

Experimental research on hydrophilic characteristics of natural soft rock at high stress state

2015 ◽  
Vol 25 (3) ◽  
pp. 489-495 ◽  
Author(s):  
Hongyun Guo ◽  
Xiangyang Lei ◽  
Yumei Zhang ◽  
Guoxing Yang ◽  
Zhang Niu
Keyword(s):  
Stress State ◽  
Experimental Research ◽  
High Stress ◽  
Soft Rock

Determination of the Biaxial Anisotropy Coefficient Using a Single Layer Sheet Metal Compression Test

2021 ◽  
Vol 883 ◽  
pp. 303-308
Author(s):  
Peter Hetz ◽  
Matthias Lenzen ◽  
Martin Kraus ◽  
Marion Merklein
Keyword(s):  
Stress State ◽  
Tensile Stress ◽  
Sheet Metal ◽  
Compression Test ◽  
Test Procedure ◽  
Rolling Direction ◽  
Single Layer ◽  
Material Behavior ◽  
Biaxial Tensile ◽  
Biaxial Tensile Stress

Numerical process design leads to cost and time savings in sheet metal forming processes. Therefore, a modeling of the material behavior is required to map the flow properties of sheet metal. For the identification of current yield criteria, the yield strength and the hardening behavior as well as the Lankford coefficients are taken into account. By considering the anisotropy as a function of rolling direction and stress state, the prediction quality of anisotropic materials is improved by a more accurate modeling of the yield locus curve. According to the current state of the art, the layer compression test is used to determine the corresponding Lankford coefficient for the biaxial tensile stress state. However, the test setup and the test procedure is quite challenging compared to other tests for the material characterization. Due to this, the test is only of limited suitability if only the Lankford coefficient has to be determined. In this contribution, a simplified test is presented. It is a reduction of the layer compression test to one single sheet layer. So the Lankford coefficient for the biaxial tensile stress state can be analyzed with a significantly lower test effort. The results prove the applicability of the proposed test for an easy and time efficient characterization of the biaxial Lankford coefficient.

scholarly journals Узагальнення моделі Голанда і Рейсснера на випадок осьової симетрії

2021 ◽  
pp. 12-19
Author(s):  
Костянтин Петрович Барахов
Keyword(s):  
Stress State ◽  
Analytical Solution ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Bessel Functions ◽  
Classical Model ◽  
Adhesive Bond ◽  
Radial Coordinate ◽  
Round Hole ◽  
Normal Stresses

The purpose of this work is to create a mathematical model of the stress state of overlapped circular axisymmetric adhesive joints and to build an appropriate analytical solution to the problem. To solve the problem, a simplified model of the adhesive bond of two overlapped plates is proposed. The simplification is that the movement of the layers depends only on the radial coordinate and does not depend on the angular one. The model is a generalization of the classical model of the connection of Holland and Reissner in the case of axial symmetry. The stresses are considered to be evenly distributed over the thickness of the layers, and the adhesive layer works only on the shift. These simplifications allowed us to obtain an analytical solution to the studied problem. The problem of the stress state of the adhesive bond of two plates is solved, one of which is weakened by a round hole, and the other is a round plate concentric with the hole. A load is applied to the plate weakened by a round hole. The discussed area is divided into three parts: the area of bonding, as well as areas inside and outside the bonding. In the field of bonding, the problem is reduced to third- and fourth-order differential equations concerning tangent and normal stresses, respectively, the solutions of which are constructed as linear combinations of Bessel functions of the first and second genera and modified Bessel functions of the first and second genera. Using the found tangential and normal stresses, we obtain linear inhomogeneous Euler differential equations concerning longitudinal and transverse displacements. The solution of the obtained equations is also constructed using Bessel functions. Outside the area of bonding, displacements are described by the equations of bending of round plates in the absence of shear forces. Boundary conditions are met exactly. The satisfaction of marginal conditions, as well as boundary conditions, leads to a system of linear equations concerning the unknown coefficients of the obtained solutions. The model problem is solved and the numerical results are compared with the results of calculations performed by using the finite element method. It is shown that the proposed model has sufficient accuracy for engineering problems and can be used to solve problems of the design of aerospace structures.

scholarly journals Calculation of Maxwell’s Equations Using MATLAB

2021 ◽  
Vol 09 (10) ◽  
Author(s):  
Subhi Abdalazim Aljily Osman ◽  
Keyword(s):  
Mathematical Method ◽  
Analytical Solution ◽  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
System Of Equations ◽  
First Order ◽  
Mathematical Programs ◽  
Mathematical Problems ◽  
Micro Radio

Maxwell’s equations describe electromagnetic Phenomena. This includes micro- , radio and radar waves .The Maxwell equations are discussed in more detail Faraday's and Amperes laws constitute a first - order hyperbolic system of equations .Matlab is one of the most famous mathematical programs in calculating mathematical problems .The aims of this study is to calculate Maxwell’s equations using Matlab .We followed the applied mathematical method by using Matlab .We found that the solution of Matlab is more accuracy and speed than the analytical solution.

scholarly journals The flexural strength of anisotropic composite plates with free edges

2021 ◽  
Vol 21 (1) ◽  
pp. 26-34
Author(s):  
Ashot G. Akopyan ◽  
Keyword(s):  
Composite Materials ◽  
Stress State ◽  
Classical Theory ◽  
Solid Mechanics ◽  
Composite Plates ◽  
Operating Conditions ◽  
Plate Bending ◽  
Structural Elements ◽  
Engineering Structures ◽  
Anisotropic Composite

Modern technology shows increased demands on the strength properties of machines, their parts, as well as various structures, reducing their weight, volume and size, which leads to the need to use anisotropic composite materials. Finding criteria to determine the ultimate strength characteristics of structural elements, engineering structures is one of the urgent problems of solid mechanics. Strength problems in structures are often reduced to finding out the nature of the local stress state at the vertices of the joints of the constituent parts. The solution of this urgent problem for composite anisotropic plates can be found in this article, where the author continues the research in this area, extending them to the bending of anisotropic composite plates. The aim of the work is to study the limit stress state of anisotropic composite plates in the framework of the classical theory of plate bending. The outer edges of the plate are considered to be free. Using the classical theory of anisotropic plate bending in the space of physical and geometric parameters, the hypersurface equations determining the low-stress zones for the edge of the contact surface of a composite cylindrical orthotropic plate are obtained. Modern technological processes of welding, surfacing, soldering and bonding allow to produce structural elements of monolithic interconnected dissimilar anisotropic materials. The combination of different materials with qualities corresponding to certain operating conditions opens up great opportunities to improve the technical and economic characteristics of machines, equipment and structures. It can contribute to a significant increase in their reliability, durability, reduce the cost of production and operation. On this basis, the solution proposed in this work can be useful to increase the strength of composite materials.

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