Design Formulas for Expansion Bellows

1981 ◽  
Vol 103 (4) ◽  
pp. 881-891 ◽  
Author(s):  
Satish Chand ◽  
S. B. L. Garg
Keyword(s):  
Mathematical Analysis ◽  
Plate Theory ◽  
Axial Loading ◽  
Beam Theory ◽  
Geometric Parameters ◽  
Equivalent Stresses ◽  
Rigorous Mathematical Analysis

In this work the problem for S-type of bellows and U-type of bellows subjected to axial loading is treated by using plate theory and beam theory. The solutions found here are compared with those obtained by rigorous mathematical analysis and simplified expressions are developed for the use of designers. The results for maximum equivalent stresses and axial deflections are plotted for different geometric parameters of bellows.

Design Nomographs of Compression Helical Springs for Predetermined Reliability Levels

1981 ◽  
Vol 103 (2) ◽  
pp. 268-273
Author(s):  
My Dao Thien ◽  
M. Massoud
Keyword(s):  
Probabilistic Approach ◽  
Design Procedure ◽  
Axial Loading ◽  
Geometric Parameters ◽  
Computer Algorithms ◽  
Mean Values ◽  
Helical Springs ◽  
Reliability Level ◽  
Classical Design ◽  
Mission Success

This paper discusses a probabilistic approach for the design of Compression Closely Coiled Helical Springs subjected to periodic axial loading. The classical design procedure results in deterministic geometric parameters with tolerances normally chosen according to standards without due regard to their effects on the mission success as normally expressed by a reliability level. With the proposed design procedure, the engineer can specify nominal mean values for the geometric parameters and their tolerances according to a predetermined reliability level. Design nomographs are presented to help the engineer, in the early stages of design, to choose between many alternatives. Computer algorithms can easily be written to verify the final or optimum design.

scholarly journals Analysis and Optimization of a Piezoelectric Energy Harvester

2019 ◽  
Vol 112 ◽  
pp. 04001 ◽  
Author(s):  
Claudia Borzea ◽  
Daniel Comeagă
Keyword(s):  
Plate Theory ◽  
Beam Theory ◽  
Finite Element Method Simulation ◽  
Ease Of Use ◽  
The Finite Element Method ◽  
Low Frequencies ◽  
Operating Modes ◽  
Piezoelectric Energy ◽  
At Resonance ◽  
Static Regime

The paper aims to assess and improve the performances of a multilayer piezoelectric MEMS device for vibrations harnessing. Two operating modes are possible: at resonance and outside resonance. In some applications it is not possible to operate at resonance, functioning being mostly at low frequencies in a quasi-static regime. An Euler-Bernoulli classic beam theory mathematical model was studied for estimating the behaviour of multilayer piezoelectric generators, in terms of deflection and voltage, at functioning under resonance frequency. The analytical results were compared with the finite element method simulation in COMSOL Multiphysics. The main goal of this study is to obtain an accurate model for engineering design purposes, with simple analytical equations and ease of use, but with predictable errors. The study proved the usefulness of the derived model but also its limitations. It also proves the need to improve the model using plate theory, for sensors with high width/height ratio.

Solution of contact problems for Gao beam and elastic foundation

2017 ◽  
Vol 23 (3) ◽  
pp. 473-488 ◽  
Author(s):  
Jitka Machalová ◽  
Horymír Netuka
Keyword(s):  
Contact Problem ◽  
Elastic Foundation ◽  
Variational Equation ◽  
Main Idea ◽  
Axial Loading ◽  
Elastic Beam ◽  
Beam Theory ◽  
Contact Problems ◽  
Problem Formulations ◽  
Nonlinear Elastic

This paper presents mathematical formulations and a solution for contact problems that concern the nonlinear beam published by Gao (Nonlinear elastic beam theory with application in contact problems and variational approaches, Mech Res Commun 1996; 23: 11–17) and an elastic foundation. The beam is subjected to a vertical and also axial loading. The elastic deformable foundation is considered at a distance under the beam. The contact is modeled as static, frictionless and using the normal compliance contact condition. In comparison with the usual contact problem formulations, which are based on variational inequalities, we are able to derive for our problem a nonlinear variational equation. Solution of this problem is realized by means of the so-called control variational method. The main idea of this method is to transform the given contact problem to an optimal control problem, which can provide the requested solution. Finally, some results including numerical examples are offered to illustrate the usefulness of the presented solution method.

Buckling of Standing Tapered Timoshenko Columns with Varying Flexural Rigidity Under Combined Loadings

2016 ◽  
Vol 16 (06) ◽  
pp. 1550017 ◽  
Author(s):  
D.-L. Sun ◽  
X.-F. Li ◽  
C. Y. Wang
Keyword(s):  
Cross Section ◽  
Timoshenko Beam ◽  
Material Properties ◽  
Flexural Rigidity ◽  
Axial Loading ◽  
Beam Theory ◽  
Shear Rigidity ◽  
Initial Value ◽  
Buckling Loads ◽  
The Stability

The stability of a nonuniform column subjected to a tip force and axially distributed loading is investigated based on the Timoshenko beam theory. An emphasis is placed on buckling of a standing column with varying cross-section and variable material properties under self-weight and tip force. Four kinds of columns with different taper ratios are analyzed. A new initial value method is suggested to determine critical tip force and axial loading at buckling. The effectiveness of the method is confirmed by comparing our results with those for Euler–Bernoulli columns for the case of sufficiently large shear rigidity. The effects of shear rigidity, taper ratio, and gravity loading on the buckling loads of a heavy standing or hanging column are examined.

Flexural Sensitivity of a V-Shaped AFM Cantilever Made of Functionally Graded Materials

2010 ◽  
Author(s):  
M. Rahaeifard ◽  
M. H. Kahrobaiyan ◽  
S. A. Moeini ◽  
M. T. Ahmadian ◽  
M. Hoviattalab
Keyword(s):  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Contact Stiffness ◽  
Beam Theory ◽  
Functionally Graded ◽  
Geometric Parameters ◽  
Graded Materials ◽  
Resonant Frequencies ◽  
Mass Distributions ◽  
Lateral Contact

In this paper, two lowest resonant frequencies and sensitivities of an AFM V-Shaped microcantilever made of functionally graded materials are studied. The beam is modeled by Euler-Bernoulli beam theory in which rotary inertia and shear deformation is neglected. It is assumed that the beam is made of a mixture of metal and ceramic with properties varying through the thickness of the beam. This variation is function of volume fraction of beam material constituents. The interaction between AFM tip and surface is modeled by two linear springs which expresses the normal and lateral contact stiffness. A relationship is developed to evaluate the sensitivity of FGM micro cantilever beam. Effect of volume fraction of materials and geometric parameters on resonant frequencies and sensitivities is studied. Results show that natural frequencies and sensitivities are significantly affected by volume fraction of material constituents and geometric parameters. Using these results, optimum geometric parameters and mass distributions of material constituents can be chosen so that high resolution images could be obtained.

scholarly journals Global Dynamics for an Age-Structured Cholera Infection Model with General Infection Rates

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 2993
Author(s):  
Xin Jiang
Keyword(s):  
Theoretical Analysis ◽  
Mathematical Analysis ◽  
Local Stability ◽  
Infection Model ◽  
Global Behavior ◽  
Uniform Persistence ◽  
Global Dynamics ◽  
Infection Rates ◽  
Age Structured ◽  
Rigorous Mathematical Analysis

This paper studies the global dynamics of a cholera model incorporating age structures and general infection rates. First, we explore the existence and point dissipativeness of the orbit and analyze the asymptotical smoothness. Then, we perform rigorous mathematical analysis on the existence and local stability of equilibria. Based on the uniform persistence, we further investigate the global behavior of the cholera infection model. The results of theoretical analysis are well confirmed by numerical simulations. This research generalizes some known results and provides deeper insights into the dynamics of cholera propagation.

scholarly journals Effect of geometric parameters and combined loading on stress distribution of tubular T-joints

Mechanika ◽  
2019 ◽  
Vol 25 (5) ◽  
pp. 350-356
Author(s):  
Samira Belhour ◽  
Hafida Kahoul ◽  
Ahmed Bellaouar ◽  
Sébastien Murer
Keyword(s):  
Axial Loading ◽  
Computation Time ◽  
Geometric Parameters ◽  
Combined Loading ◽  
Offshore Platforms ◽  
Tubular Structures ◽  
Stress Concentrations ◽  
Standard Samples ◽  
T Joints ◽  
Modeling And Analysis

Steel tubular structures are widely used in the construction of offshore platforms and T-type junctions are extensively used in this domain. The tubular members are welded, which generates significant stress concentrations at the edges. The stress levels reached in these critical places are used to assess lifetimes based on fatigue curves from tests conducted on standard samples. This study is devoted to the modeling and analysis of T-type welded tubular structures for the determination of hot spots stresses (HSS) at the chord/brace intersection, A numerical analysis was carried out to study the effect of a combined loading composed of an axial loading and a continuation of rational bending, that best assimilate real conditions, as well as the effect of normalized geometric parameters α, β, g on the distribution of stress concentration (area and values) of T-joints. The mechanical behaviour has been modeled in 2D using quadrangular and triangular thin-shell elements by the finite element method (FEM). It is the most appropriate approach because it considers all geometric complexities and singularities of the structure, while the efforts as well as the computation time are considerably reduced compared to an experimental study or to complex FE models implementing solid elements. In this study, we use the COMSOL-MULTIPHYSICS® software...

scholarly journals Geometrical Model of Spiking and Bursting Neuron on a Mug-Shaped Branched Manifold

2020 ◽  
Vol 30 (15) ◽  
pp. 2030044
Author(s):  
Mohamed Gheouali ◽  
Tounsia Benzekri ◽  
René Lozi ◽  
Guanrong Chen
Keyword(s):  
Mathematical Analysis ◽  
Phenomenological Model ◽  
Geometrical Model ◽  
Dynamic Motion ◽  
Bursting Neuron ◽  
Theoretical Results ◽  
Rigorous Mathematical Analysis

Based on the Hodgkin–Huxley and Hindmarsh–Rose models, this paper proposes a geometric phenomenological model of bursting neuron in its simplest form, describing the dynamic motion on a mug-shaped branched manifold, which is a cylinder tied to a ribbon. Rigorous mathematical analysis is performed on the nature of the bursting neuron solutions: the number of spikes in a burst, the periodicity or chaoticity of the bursts, etc. The model is then generalized to obtain mixing burst of any number of spikes. Finally, an example is presented to verify the theoretical results.

Case Study of the Effect of Combined Axial and Lateral Loadings on the Critical Buckling Capacity of Piping Supports

2020 ◽  
Author(s):  
Phillip Wiseman ◽  
Alex Mayes ◽  
Shreeya Karnik
Keyword(s):  
Large Deformation ◽  
Axial Loading ◽  
Beam Theory ◽  
Second Order ◽  
Lateral Acceleration ◽  
Bernoulli Beam ◽  
Deformation Method ◽  
Closed Form Solutions ◽  
Bernoulli Beam Theory ◽  
Euler Bernoulli Beam

Abstract Snubbers are used in industry to restrain piping in dynamic events which can see significant axial loading as well as lateral acceleration. Snubbers are often employed with an extension when required to bridge gaps between the piping and building structure. As a result, they are susceptible to buckling instability issues. The pipe support and restraint design by analysis buckling criteria for supports given within the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code, Section III, Division 1, Subsection NF is investigated to determine the behavior of snubber assemblies under combined axial and lateral loadings. Four types of analyses are performed on the assemblies under the action of axial loading to demonstrate finite element and closed form solutions. These include the following: linear Eigen buckling, nonlinear second order large deformation method, energy method and Euler Bernoulli beam theory. In addition, a variety of snubber assembly sizes are subjected to combined axial and lateral loading in the form of multiple magnitudes of lateral acceleration. The behavior was analyzed by the Euler Bernoulli beam theory and nonlinear second order large deformation method. The techniques of each method are compared providing explanations of the assumptions taken, relevant limitations and recommended applications.

The Effect of Chucking Methods on Roundness Error in the Boring Process

1976 ◽  
Vol 98 (1) ◽  
pp. 233-238 ◽  
Author(s):  
C. H. Kahng ◽  
H. W. Lord ◽  
T. L. Davis
Keyword(s):  
Theoretical Model ◽  
Beam Theory ◽  
Geometric Parameters ◽  
Curved Beam ◽  
Roundness Error ◽  
Cylindrical Workpiece ◽  
Analytical Expressions ◽  
Good Agreement

Curved-beam theory is used to obtain a theoretical model to describe deformations in a cylindrical workpiece during boring processes. Analytical expressions are obtained for roundness error due to two-, three-, and four-jaw chucks. Experiments are carried out and theory is compared with measured values of roundness errors for several combinations of material and geometric parameters, showing good agreement.

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