Thermoelasticity Solutions for Straight Beams

2002 ◽  
Vol 69 (3) ◽  
pp. 224-229 ◽  
Author(s):  
C. D. Copper ◽  
W. D. Pilkey
Keyword(s):  
Temperature Distribution ◽  
Cross Section ◽  
Solution Technique ◽  
Shear Stresses ◽  
Stress Distributions ◽  
Strength Of Materials ◽  
Numerical Efficiency ◽  
Temperature Distributions ◽  
Normal And Shear Stresses

This paper presents a thermoelastic solution technique for beams with arbitrary quasi-static temperature distributions that create large transverse normal and shear stresses. This technique calculates the stress resultants and centroid displacements along a beam. Then, the stress resultants and temperature distribution are used to calculate the stress distributions on a cross section of the beam. Simple examples demonstrate the numerical efficiency of the proposed technique and the inadequacy of the strength of materials theory to solve these types of problems.

Deflection of a Thick Ring in Diametral Compression by Test and by Strength-of-Materials Theory

1959 ◽  
Vol 26 (2) ◽  
pp. 294-295
Author(s):  
Alexander Blake
Keyword(s):  
Cross Section ◽  
Strain Energy ◽  
Rectangular Cross Section ◽  
Theoretical Estimate ◽  
Shear Stresses ◽  
Strength Of Materials ◽  
Diametral Compression ◽  
Normal And Shear Stresses

Abstract Experimental and theoretical deflection studies are briefly described for several steel rings, of uniform rectangular cross section, compressed by two forces along a diameter and having D/d ratios ranging from 1.3 to 1.9. The calculations are based on the principle of Castigliano and expressions for strain energy due to bending, normal, and shear stresses. Discrepancies between the theoretical estimate and the tests are shown.

scholarly journals The elastic equilibrium of isotropic plates and cylinders

1949 ◽  
Vol 195 (1043) ◽  
pp. 533-552 ◽  
Keyword(s):  
Fourier Series ◽  
General Solution ◽  
Power Series ◽  
Elastic Equilibrium ◽  
Shear Stresses ◽  
Stress Distributions ◽  
Isotropic Plates ◽  
First Approximation ◽  
Stress Components ◽  
Normal And Shear Stresses

A general solution of the elastic equations is obtained for problems of stress distributions in plates or cylinders when the bounding faces of the plates Z = ± h , or the flat ends of the cylinders, are free from applied normal and shear stresses. The solution is expressed either in the form of Fourier series in the co-ordinate Z , or in power series in Z , the coefficients of the series being certain functions of the x and y co-ordinates which are sufficient to satisfy boundary conditions over two bounding cylindrical surfaces normal to the planes Z = ± h . The form of the theory is greatly simplified by making use of complex combinations of stress components, and by using the complex variable z = x + iy . A first approximation to the part of the theory which deals with the bending of the plate yields a theory similar in character to that given recently by Reissner.

General Design of Hollow RC Sections under Combined Actions

2019 ◽  
Author(s):  
Kenneth C. Kleissl ◽  
J. L. Domingues Costa
Keyword(s):  
Beam Theory ◽  
Design Tool ◽  
Easy Access ◽  
Shear Stresses ◽  
Stress Distributions ◽  
Structural Capacity ◽  
One Step ◽  
Combined Actions ◽  
Large Material ◽  
Normal And Shear Stresses

<p>Hollow reinforced concrete sections are consistently considered the preferred solution for medium to large sized bridge projects due to its structural efficiency and the large material savings associated with it.</p><p>To fully harvest the structural capacity of hollow sections exposed to combined actions it is necessary to leave behind the simplicity of treating the verification of structural adequacy for normal stresses (beam theory) separately from that of shear stresses (diagonal truss model) and instead fully exploit the advantages of choosing more efficient stress distributions. By exploring the vast possibilities of other statically admissible systems using optimization routines, one will find that longitudinal reinforcement near the neutral axis can be utilized much more efficiently.</p><p>In addition, by adhering to the interdependency constraints between normal and shear stresses a much more precise picture of the actual service stress state can be determined. There is therefore the need for a one- step, automated design tool capable of addressing such verifications holistically.</p><p>In this paper the theoretical basis and a free to use open-source design tool is presented, allowing for easy access to highly optimized designs capable of pushing the materials to their limits.</p>

On the Stresses in Hooks, and Their Determination by Relaxation Methods

1946 ◽  
Vol 155 (1) ◽  
pp. 1-19 ◽  
Author(s):  
L. Fox ◽  
R. V. Southwell
Keyword(s):  
Cross Section ◽  
Inverse Method ◽  
Formal Solution ◽  
Circular Cross Section ◽  
Shear Stresses ◽  
Stress Distributions ◽  
Relaxation Methods ◽  
Stress Functions

The “semi-inverse” method of Saint Venant has been applied to hooks by Golovin (1881)‡ and by Southwell (1942). The actual hook is replaced in calculation by a half-tore sustaining shear stresses appropriately distributed over its terminal sections, and having a cross-section identical with the principal section of the hook (shaded in Fig. 1). Golovin's solution was for a narrow rectangular hook; Southwell's is a formal solution applicable to any shape of section, and involves two stress-functions related by three conditions at the boundary. In the present paper, stress distributions are determined on the basis of Southwell's solution for two B.S.I. standard hooks, the first of “trapezoidal” and the second of circular cross-section. The results are exhibited in Figs. 3–6.

Naturally Twisted Layered Anisotropic Rod Made of Reinforced Materials Research

2015 ◽  
Vol 736 ◽  
pp. 30-38 ◽  
Author(s):  
Alibek Nurimbetov ◽  
Amangeldy Bekbayev ◽  
Seitzhan Orynbayev ◽  
Muratkali Dzhamanbayev ◽  
Meruyert Keikimanova
Keyword(s):  
Cross Section ◽  
Strain State ◽  
Rectangular Cross Section ◽  
Shear Stresses ◽  
Anisotropy Coefficient ◽  
Centrifugal Forces ◽  
Materials Research ◽  
Limit Stress ◽  
The Individual ◽  
Normal And Shear Stresses

In this paper, we consider the deformation of multilayer bars in torsion and tension. Thus, in the analyzed strength calculations rod having a rectangular cross section of the composite material. Namely, the choice of the structure of the material, satisfy the specifications of the rod in terms of stress-strain state in a torsion-bending coherence taking into account features of the composite materials. On the example with a layered core, being under the influence of centrifugal forces shows the effect of shifts between the layers on the redistribution of normal and shear stresses in layers. Depending on the magnitude of the anisotropy coefficient of the material used, normal and shear stresses in the outer layers is increased by 2-5 times. Comparison of these values ​​with limit stress for these layers allows you to select how the reinforcement of these layers. Collection of data about the influence of the stiffness of the individual layers by an angle promotion rod and durability allow the optimal folding of the reinforcing layers and the type of reinforcement and matrix.

Numerical Simulation of the Temperature Distribution during the Metal Laser Sintering of Parts

2009 ◽  
Vol 16-19 ◽  
pp. 475-479 ◽  
Author(s):  
Chang J. Wang ◽  
Ibiye A. Roberts ◽  
Diane J. Mynors
Keyword(s):  
Numerical Simulation ◽  
Temperature Distribution ◽  
Thermal Stresses ◽  
Laser Sintering ◽  
Residual Stress Distribution ◽  
Powder Layer ◽  
Stress Distributions ◽  
Metal Powders ◽  
Simulation Process ◽  
Temperature Distributions

The Metal Laser Sintering (MLS) process has been developed over the last decade to produce 3D parts from CAD files using metal powders. A considerable amount of research has been conducted into the melting and solidifying process of metal powders, mainly to predict the temperature distribution in a single metal powder layer or a few layers. The temperature and thermal residual stress distribution in real parts built using MLS has rarely been reported. Finite element simulations of temperature distributions in metal powders and parts requires huge computing resources, this is the main obstacle to successfully predicting temperature and thermal stress distributions in MLS parts. However, from the numerical results in this paper, the periodic nature of temperature distributions in parts around the laser spot can be used to simplify the numerical simulation process to achieve the prediction of temperature and thermal stresses distributions in parts built by MLS.

Finite Element Analysis of Tire/Rim Interface Forces Under Braking and Cornering Loads

1992 ◽  
Vol 20 (2) ◽  
pp. 83-105 ◽  
Author(s):  
J. P. Jeusette ◽  
M. Theves
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Contact Pressure ◽  
Element Model ◽  
Shear Stresses ◽  
Detailed Knowledge ◽  
Stress Distributions ◽  
Element Analysis ◽  
Plane Shear ◽  
Normal Contact

Abstract During vehicle braking and cornering, the tire's footprint region may see high normal contact pressures and in-plane shear stresses. The corresponding resultant forces and moments are transferred to the wheel. The optimal design of the tire bead area and the wheel requires a detailed knowledge of the contact pressure and shear stress distributions at the tire/rim interface. In this study, the forces and moments obtained from the simulation of a vehicle in stationary braking/cornering conditions are applied to a quasi-static braking/cornering tire finite element model. Detailed contact pressure and shear stress distributions at the tire/rim interface are computed for heavy braking and cornering maneuvers.

scholarly journals Ultrasonic Deicing Efficiency Prediction and Validation for a Flat Deicing System

2020 ◽  
Vol 10 (19) ◽  
pp. 6640
Author(s):  
Zhonghua Shi ◽  
Zhenhang Kang ◽  
Qiang Xie ◽  
Yuan Tian ◽  
Yueqing Zhao ◽  
...  
Keyword(s):  
Lead Zirconate Titanate ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Lead Zirconate ◽  
Efficiency Factor ◽  
Zone Model ◽  
Shear Stresses ◽  
Stress Distributions ◽  
Total Energy Density ◽  
Average Shear

An effective deicing system is needed to be designed to conveniently remove ice from the surfaces of structures. In this paper, an ultrasonic deicing system for different configurations was estimated and verified based on finite element simulations. The research focused on deicing efficiency factor (DEF) discussions, prediction, and validations. Firstly, seven different configurations of Lead zirconate titanate (PZT) disk actuators with the same volume but different radius and thickness were adopted to conduct harmonic analysis. The effects of PZT shape on shear stresses and optimal frequencies were obtained. Simultaneously, the average shear stresses at the ice/substrate interface and total energy density needed for deicing were calculated. Then, a coefficient named deicing efficiency factor (DEF) was proposed to estimate deicing efficiency. Based on these results, the optimized configuration and deicing frequency are given. Furthermore, four different icing cases for the optimize configuration were studied to further verify the rationality of DEF. The effects of shear stress distributions on deicing efficiency were also analyzed. At same time, a cohesive zone model (CZM) was introduced to describe interface behavior of the plate and ice layer. Standard-explicit co-simulation was utilized to model the wave propagation and ice layer delamination process. Finally, the deicing experiments were carried out to validate the feasibility and correctness of the deicing system.

Stress concentration factors for the torsion of curved beams of arbitrary cross-section

2006 ◽  
Vol 220 (12) ◽  
pp. 1709-1726 ◽  
Author(s):  
R E Cornwell
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Stresses ◽  
Curved Beams ◽  
Finite Element Implementation ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

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