Exact Solutions For Stresses Research Articles

Significance of peripheral layer: the case of mucus flow through a ciliated tube using Rabinowitsch model

Modern medicine has taken energy loss during cilia beating in the human stomach, which under some circumstances causes blood flow to become acidic, very seriously. In current report covering a whole advancement and results for the impact of Rabinowitsch model with cilia-driven flow analysis with the help of ciliary beating in a cylindrical tube. The fluid is incompressible, and layers of fluid do not mix. The fluid flow with heat and mass transfer is firstly modeled in wave and then transformed into fixed frame. Exact solutions for stresses, temperature velocity, and concentration profiles whereas numerical pressure rise is obtained subject to relevant boundary conditions. The behavior of incipient parameters is shown graphically (plotted in MATHEMATICA 13.0) in the results section. The key findings obtained from graphical results show that maximum magnitude for velocity and temperature is achieved in middle layer of fluid whereas in the outer layer concentration profile is maximum. The current study may help researchers to develop new treatments for diseases such as cystic fibrosis, in which impaired ciliary function leads to mucus accumulation in the lungs. The attained exact and numerical outcomes are novel and offered here for first time in literature.

Thermal and concentration analysis of two immiscible fluids flowing due to ciliary beating

This article explores the flow properties with mass and heat transfer of multilayered flow of two immiscible fluids (Phan-Thien-Tanner and Jeffrey fluid models) flowing due to ciliary beating in a channel, which is beneficial in different applications related to bioengineering, biomedical sciences, and medical equipment. Ciliated epithelium in airways is covered with airway surface liquid, which is mainly composed of two different layers. The first one is the mucus layer (Phan-Thien-Tanner fluid), which is a non-Newtonian, viscoelastic fluid, and the second layer is the periciliary liquid layer, which is considered the Jeffery fluid model. The fluid is considered to be incompressible, and layers of fluid do not mix with each other. The fluid flow with mass and heat transfer is first modeled as a wave and then transformed into a fixed frame. Exact solutions for stresses, velocity, temperature, and concentration profiles are obtained by simple integration. The behavior of emerging factors is shown graphically (plotted in MATHEMATICA 13.0) in the results section. The key findings from the graphical results show that the middle layer of fluid has the greatest magnitude for velocity and temperature, while the outer layer has the greatest concentration profile. This analysis may be helpful in keeping the airways clear from inhaled pollutants like viruses and bacteria.

Failure analysis of biocomposite sandwich pipe under internal pressure – Application for high pressure gas transportation pipelines MEDGAZ

In this paper, analytical and 3D numerical models are developed to investigate the mechanical behavior of sandwich pipe under internal pressure loading. The suggested models provide an exact solution for stresses, strains and displacement on the sandwich pipe, which is made of epoxy material for the core layer and reinforced materials with an alternate-ply for the skin layers. The aim of this analysis is to evaluate the potential applications of jute and pineapple leaf fiber (PALF) bio-fibers in order to replace glass synthetic fibers generally employed in sandwich pipes. In this subject, a failure analytical analysis was developed using TSAI-WU criterion. The results of stress, strain and displacement distribution through the thickness are presented for the analytical and numerical models. The comparison between the both models results show a very good agreement. In order to increase the rigidity of a biocomposite sandwich and reduce the gap compared with a synthetic sandwich, a gradual reinforcing of layer numbers was chosen, which permitted the best behavior. The ultimate pressure and safety factors obtained by increasing biocomposite layers are significant for composite transportation pressure pipelines, especially for sandwich pipe based on PALF/epoxy.

Buckling problems of patch loaded plates with and without stiffeners – analytical approach

AbstractGeneralized analytical approach, with exact stress solutions, to buckling problems of in‐plane loaded plate with and without stiffeners has been presented through the case of locally distributed direct stresses. Several mathematical models have been chosen to represent high webs of steel girders under the patch load. Initially, the basic model has been built to simulate a girder used in the experimental research where the external load is equilibrated by support reactions. The second, more complex model included shear stresses along vertical stiffeners with a task to equilibrate the external loads, simulating a single web segment between the stiffeners of a long girder. The upgrade of the second model by adding a longitudinal stiffener resulted in the third model. Considering the complexity of stress distributions within the plate under such a demanding load, an analytical model for these problems has not been presented earlier. For the first time the influence of flexural stiffeners' rigidity on the plate buckling has been analysed with the exact solutions for in‐plane stress distributions, for simply supported plate. Results confirm the high quality of the analytical solution for the first and the second model and speak in favour of this approach and its potential for further upgrading in the case of the third model.

Revisiting classic problems of exact solutions for stresses in functionally graded pressure vessels

In 2001, Naki Tutuncu and Murat Ozturk obtained analytical solutions for stress distribution of functionally graded material (FGM) cylindrical and spherical pressure vessels [COMPOS. PART. B-ENG, 32(8):683–686 (2001)]. The previous paper belongs to the classical study of elastic mechanics analysis of FGM, but their analytical expressions for the circumferential stress have some errors. The present letter corrects some analytical solutions in the classic problems of exact solutions for stresses in functionally graded pressure vessels. We prove correctness of the proposed analytical solutions by comparing with classical theory and finite element results.

Thermo-mechanical analysis and optimization of functionally graded rotating disks

The behavior of thermo-mechanical stresses in functionally graded axisymmetric rotating hollow disks with variable thickness is analyzed. The material is assumed to be functionally graded in the radial direction. First, a two-dimensional axisymmetric model of the functionally graded rotating disk is developed using the finite element method. Exact solutions for stresses are then obtained assuming that the plane theory of elasticity holds. These solutions are in accordance with finite element ones, thus showing the validity of the assumption. Finally, in order to reduce the maximum equivalent stress along the radius, the optimization of the material distribution is addressed. To avoid subsequent finite element simulations in the optimization process, which can be computationally demanding, a nonlinear constrained optimization problem is proposed, for which the solution is obtained numerically by the sequential quadratic programming method, showing prominent results in terms of equivalent stress uniformity.

Deformation of a rectangular plate with an arbitrarily located circular hole under in-plane pure shear loading

Exact solutions for stresses, strains, displacements, and the stress concentration factors of a rectangular plate perforated by an arbitrarily located circular hole subjected to in-plane pure shear loading are investigated by two-dimensional theory of elasticity using the Airy stress function. The hoop stresses, strains, and displacements occurring at the edge of the circular hole are computed and plotted. Comparisons are made for the hoop stresses and the stress concentration factors from the present study and those from a rectangular plate with a circular hole under uni-axial and bi-axial uniform tensions and in-plane pure bending moments on two opposite edges.

Closed-form solution of the Ogden–Hill’s compressible hyperelastic model for ramp loading

This article deals with the visco-hyperelastic modelling approach for compressible polymer foam materials. Polymer foams can exhibit large elastic strains and displacements in case of volumetric compression. In addition, they often show significant rate-dependent properties. This material behaviour can be accurately modelled using the visco-hyperelastic approach, in which the large strain viscoelastic description is combined with the rate-independent hyperelastic material model. In case of polymer foams, the most widely used compressible hyperelastic material model, the so-called Ogden–Hill’s model, was applied, which is implemented in the commercial finite element (FE) software Abaqus. The visco-hyperelastic model is defined in hereditary integral form, therefore, obtaining a closed-form solution for the stress is not a trivial task. However, the parameter-fitting procedure could be much faster and accurate if closed-form solution exists. In this contribution, exact stress solutions are derived in case of uniaxial, biaxial and volumetric compression loading cases using ramp-loading history. The analytical stress solutions are compared with the stress results in Abaqus using FE analysis. In order to highlight the benefits of the analytical closed-form solution during the parameter-fitting process experimental work has been carried out on a particular open-cell memory foam material. The results of the material identification process shows significant accuracy improvement in the fitting procedure by applying the derived analytical solutions compared to the so-called separated approach applied in the engineering practice.

Theoretical analysis of earth pressure against rigid retaining walls under translation mode

The soil mass behind a retaining wall gradually yields and separates from the stationary soil mass with the complex shape of the slip surface depending on the mode of wall movement and roughness of the wall surface. In this study, the problem of a rigid retaining wall with a uniform surcharge acting along the horizontal backfill under active translation mode is investigated in a two-dimensional system of equilibrium. Exact stress solutions based on Janssen׳s approach are generalized in rectangular coordinates and are validated with boundary conditions on the retaining wall and at the Coulomb slip line behind the wall. Because the yield condition is not used in Janssen׳s approach, the proposed solution is a merely static stress solution, not statically admissible solution. New equations are developed to estimate the magnitude and distribution of vertical, horizontal and shear stresses in the failure zone behind a retaining wall. The proposed analysis indicates the arching effect behind the retaining wall because the maximum stresses do not appeared at the toe; but at some distance away from the toe of the retaining wall. The results of the proposed formulations are compared with both full-scale and laboratory-scale experimental data as well as the existing formulations. The proposed analysis provides comparable approximations for horizontal active stress distribution, the magnitude and the application height of the horizontal active force at the wall.

Exact deformation of an infinite rectangular plate with an arbitrarily located circular hole under in-plane loadings

Exact solutions for stresses, strains, and displacements of a perforated rectangular plate by an arbitrarily located circular hole subjected to both linearly varying in-plane normal stresses on the two opposite edges and in-plane shear stresses are investigated using the Airy stress function. The hoop stress occurring at the edge of the non-central circular hole are computed and plotted. Stress concentration factors (the maximum non-dimensional hoop stresses) depending on the location and size of the non-central circular hole and the loading condition are tabularized.

Exact deformation of a rectangular plate with a central circular hole under in-plane loads

Exact solutions for stresses, strains, and displacements of a perforated rectangular plate by a central circular hole under both linearly varying in-plane normal stresses on two opposite edges and in-plane shear stresses acting on its entire outer boundary are investigated using the Airy stress function. The hoop stresses arising at the edge of the circular hole are also calculated and plotted. Stress concentration factors (the maximum non-dimensional hoop stresses) depending upon the size of the circular hole and the inplane loading condition are tabularized.

Exact solutions for stresses, strains, and displacements of a rectangular plate with an arbitrarily located circular hole subjected to in-plane bending moment

Exact solutions for stresses, strains, and displacements of a rectangular plate with arbitrarily located circular hole subjected to in-plane bending moment are investigated by two-dimensional theory of elasticity using the Airy stress function. The present method of analysis is much simpler, but it produces an exact solution, which is its great strength, than the methods used by previous researchers. The hoop stresses occurring at the edge of the non-central circular hole are computed and plotted. The stress concentration factors (the maximum non-dimensional hoop stresses) depending on the location and size of the non-central circular hole are tabularized.

Steady-State Creep Deformations and Stresses in FGM Rotating Thick Cylindrical Pressure Vessels

AbstractIn the present study, a closed-form analytical solution for the steady-state creep stresses of rotating thick cylindrical pressure vessels made of functionally graded materials (FGMs) is carried out. Norton's law governs the creep response of the material. Exact solutions for stresses and strain rate are obtained under the plane strain condition. How different material parameters involved in Norton's law affect radial and circumferential stresses together with the equivalent strain rate in rotating thick-walled cylindrical vessels under internal pressure is investigated. The result obtained shows that the property of FGMs has a significant influence on the equivalent creep strain rate and stresses distributions along the radial direction.

Exact Solutions for Stresses, Strains, and Displacements of a Rotating Annular Plate with Variable Thickness Subjected to a Centrifugal Body Force

AbstractThe author has discovered several errors that are not typographical in a famous governing differential equation and its general solution. The purpose of the current study is to reveal the errors, correct them, and present some numerical results.

Exact solutions of stresses, strains, and displacements of a perforated rectangular plate by a central circular hole subjected to linearly varying in-plane normal stresses on two opposite edges

Exact solutions for stresses, strains, and displacements of a perforated rectangular plate by a central circular hole subjected to linearly varying in-plane normal stresses on two opposite edges are investigated by two-dimensional theory of elasticity using the Airy stress function . The hoop stresses , strains, and displacements occurring at the edge of the circular hole are computed and plotted. Comparisons are made for the stress concentration factors for several types of linearly varying in-plane loading. • We analyze perforated plates by a central circular hole. • The plate is subjected to linearly varying in-plane normal stress. • We use the two-dimensional theory of plane elasticity using the Airy stress function. • We obtain exaction solutions for stress, strain, and displacement.

Analytical Study for Electromagnetothermoelastic Behavior of a Functionally Graded Piezoelectric Solid Cylinder

Analytical study for electromagnetothermoelastic behavior of a solid cylinder composed of functionally graded piezoelectric material (FGPM), placed in a uniform magnetic field, subjected to electric, thermal, and mechanical loadings is presented. For the case that material properties obey an identical power law, exact solutions for stresses and perturbation of magnetic field vector in the FGPM solid cylinder are determined by using the theory of electromagnetothermoelasticity. Numerical examples and some useful discussions are presented to show the significant influence of material inhomogeneity; adopting a certain value of the inhomogeneity parameter and applying suitable loads can optimize the FGPM solid cylindrical structures.

Exact Solutions for Stresses, Strains, Displacements, and Stress Concentration Factors of a Perforated Rectangular Plate by a Circular Hole Subjected to In-Plane Bending Moment on Two Opposite Edges

Exact solutions for stresses, strains, displacements, and the stress concentration factors of a perforated rectangular plate by a circular hole subjected to in-plane bending moment on two opposite edges are investigated by two-dimensional theory of elasticity using the Airy stress function. The hoop stresses, strains, and displacements occurring at the edge of the circular hole are computed and plotted. Comparisons are made for the hoop stresses and the stress concentration factors from the current study and rectangular plates with a circular hole under uniaxial and biaxial uniform tensions and pure shear loading.

Determination of Stress Intensity Factor for Cracked Brazilian Disc Using Weight Function

To reduce stress concentration near the loading point, Brazilian test, normally used for the indirect determination of tensile strength for rock or concrete quasi-brittle materials, is usually subjected to uniformly distributed pressure over finite width (or arc) of the Brazilian disc. As an extension, the same geometry, in which a central notch is introduced in the symmetrical plane of applied forces, can be used to determine fracture toughness of the materials. For this purpose, accurate expression for stress intensity factor (SIF) for central cracked Brazilian disc should be provided first. To this end, weight function method is used in this paper where weight function for central cracked disc is available in general SIF handbooks. Meanwhile, the exact stress solution in the intact Brazilian disc subjected to uniformly distributed pressure is derived by use of numerical method. In the end, some finite element analysis is carried out using the program package ABAQUS on the Brazilian disc, and the comparison results regarding the SIF between the weight function method and numerical method prove the validity of the proposed method.

An exact solution for stresses and displacements of pressurized FGM thick-walled spherical shells with exponential-varying properties

Exact closed-form solutions have been derived for stresses and the displacements in thick spherical shells made of functionally graded materials with exponential-varying properties subjected to internal and external pressure. Poisson’s ratio is assumed to be constant. The obtained results show that the inhomogeneity properties of FGMs have a significant influence on the displacement and stresses distribution along the radial direction. A numerical solution using finite element method is also presented and good agreement was found between the analytical solutions and the solutions carried out through the FEM. The values used in this study are arbitrarily chosen to demonstrate the effect of inhomogeneity on displacements and stresses distributions.

Coupled Structural/Thermal Analysis of Cylindrical Part of Multilayered Composite Vessel

This paper focuses on the coupled structural/thermal response of a cylindrical part of multi-layered composite vessel. Uniform and parabolic temperature distributions are chosen for the structural loads. In this work, an analytical model is proposed in which the laminate composite is assumed to be an anisotropic purely elastic material. Assuming that the interface between the core and skin are perfectly bound, continuity conditions for the displacement and stress, the suggested analytical model provides an exact solution for stresses and strains on the cylindrical section of the vessel solution submitted hygrothermal loading coupled with internal pressure with end effect.