Stress Concentrations in Thin Spherical Shells

1966 ◽  
Vol 88 (2) ◽  
pp. 231-236 ◽  
Author(s):  
Egor P. Popov ◽  
Joseph Penzien ◽  
Mandayam K. S. Rajan
Keyword(s):  
Axial Load ◽  
Shear Load ◽  
Stress Distributions ◽  
Stress Concentrations ◽  
Spherical Shells ◽  
Practical Applications ◽  
Small Deflection ◽  
External Moment ◽  
Rigid Insert ◽  
Deflection Theory

Stress distributions occurring in the proximity of rigid circular inserts attached to thin spherical shells are reported in this paper. The solutions are achieved by employing conical coordinates tangent to the sphere at its intersection with the insert. A small-deflection theory is used and results are stated in terms of readily available functions. For convenience in practical applications, solutions for several loading conditions are carried through to completion. Specifically, the paper gives formulas for stress distributions occurring in a spherical shell when provided with a rigid insert and when subjected to (a) internal pressurization in the shell; (b) axial load on the insert; (c) external moment on the insert; and (d) tangential shear load on the insert. The necessary constants of integration are given in tables and the procedure developed is illustrated by a comprehensive example.

The Mixed-Body Model: A Method for Predicting Large Deflections in Stepped Cantilever Beams

2021 ◽  
pp. 1-18
Author(s):  
Brandon Sargent ◽  
Collin Ynchausti ◽  
Todd G Nelson ◽  
Larry L Howell
Keyword(s):  
Large Deflections ◽  
Cantilever Beams ◽  
Element Analysis ◽  
Body Model ◽  
Minimal Error ◽  
Small Deflection ◽  
Rigid Body Model ◽  
Expected Values ◽  
Deflection Theory ◽  
Sample Set

Abstract This paper presents a method for predicting endpoint coordinates, stress, and force to deflect stepped cantilever beams under large deflections. This method, the Mixed-Body Model or MBM, combines small deflection theory and the Pseudo-Rigid-Body Model for large deflections. To analyze the efficacy of the model, the MBM is compared to a model that assumes the first step in the beam to be rigid, to finite element analysis, and to the numerical boundary value solution over a large sample set of loading conditions, geometries, and material properties. The model was also compared to physical prototypes. In all cases, the MBM agrees well with expected values. Optimization of the MBM parameters yielded increased agreement, leading to average errors of <0.01 to 3%. The model provides a simple, quick solution with minimal error that can be particularly helpful in design.

Study on Deformation and Stress of CRCP under Concentrated Vertical Load with Hollow Foundation

2011 ◽  
Vol 250-253 ◽  
pp. 3415-3420
Author(s):  
Xiao Bing Chen ◽  
Xiao Ming Huang ◽  
Jin Hu Tong
Keyword(s):  
Equivalence Principle ◽  
Transverse Crack ◽  
Torsion Theory ◽  
Slab Thickness ◽  
Vertical Load ◽  
Effective Measure ◽  
Small Deflection ◽  
Half Wave ◽  
Elastic Thin Plate ◽  
Deflection Theory

Based on the equivalence principle, the concentrated vertical load which acts on the Continuously Reinforced Concrete Pavement(CRCP) transverse crack is translated into the equivalent half-wave sine load by Fourier transform. According to the translation principle of the force, the half-wave sine vertical load acting on the CRCP transverse crack is decomposed to the half-wave sine vertical load and the torsion force acting on the center of CRCP. Lastly, the deflection, torsional displacement and stress formulas of CRCP under the concentrated vertical load with hollow foundation are put forward, which is on the basis of the small deflection theory of elastic thin plate and torsion theory. The results show that increasing the slab thickness is the most effective measure to reduce maximal deflection, distortion displacement and stress of CRCP concentrated vertical load with hollow foundation.

scholarly journals ANALISIS PENGARUH BENTUK DAN LOKASI BUKAAN PADA BALOK TINGGI MENGGUNAKAN METODE ELEMEN HINGGA

2020 ◽  
Vol 3 (4) ◽  
pp. 1209
Author(s):  
Anthony Fariman ◽  
Leo S. Tedianto
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Wall Structure ◽  
Deep Beam ◽  
Stress Distributions ◽  
Stress Concentrations ◽  
Offshore Structure ◽  
Deep Beams ◽  
Concentrated Load ◽  
Cable Networks

ABSTRAKBalok tinggi beton bertulang merupakan salah satu struktur khusus yang dapat memikul beban cukup besar dan umumnya digunakan sebagai transfer girder, struktur lepas pantai, struktur dinding, dan pondasi. Kehadiran bukaan pada balok tinggi dapat memfasilitasi jalur saluran AC, saluran pipa, jaringan kabel dan lain-lain. Dengan adanya bukaan pada balok tinggi dapat memberikan beberapa efek samping yaitu terjadinya diskontinuitas geometri, tegangan terdistribusi non-linier pada balok tinggi, berkurangnya kekuatan dari balok, dan timbulnya konsentrasi tegangan di sekitar bukaan. Penelitian ini bertujuan untuk menganalisis efek dari kehadiran bukaan pada balok tinggi di atas dua perletakan (sendi-rol) dan dibebani beban terpusat di tengah bentang balok lalu memvariasikan bentuk bukaan (persegi, persegi panjang, dan lingkaran) dan lokasi bukaan. Tegangan lentur pada balok tinggi dan konsentrasi tegangan yang terjadi di sekitar bukaan merupakan hal yang akan dibahas dalam penelitian. Analisis akan dibantu dengan Midas FEA yang merupakan program berbasis elemen hingga dan  pemodelan dilakukan dengan elemen solid tiga dimensi. Hasil dari analisis ini menunjukkan bahwa kehadiran bukaan pada balok tinggi menyebabkan kenaikan tegangan secara signifikan. Lokasi dari bukaan yang mendekati daerah tengah bentang balok juga sangat mempengaruhi besarnya tegangan yang terjadi.ABSTRACTReinforced concrete deep beam is one of the special structures that can carry quite a big load and generally used as a transfer girder, offshore structure, wall structure, and foundation. The appearance of openings in deep beams can facilitate AC pipelines, plumbing pipes, cable networks, etc. The existence of openings in deep beams can provide a few side effects such as geometric discontinuity, non-linear stress distributions over the deep beams, reduced strength of the deep beams, and stresses concentration will emerged around the openings. The purpose of this research is to analyze the effects from the existence of openings in deep beams on two supports (hinge and roller) and loaded by concentrated load in mid-span then variate the shape of openings (square, rectangle, and circle) and location of the openings. Flexural stresses in deep beams and the stress concentrations that occur around the openings are discussed in this research. The analysis will be assisted by Midas FEA which is a finite element based program and modelling will be executed in three dimensional solid elements. The result of this analysis showed that the existence of the openings in deep beams can cause stresses to increase significantly high. The location of the openings close to the mid-span of the deep beams also affect the amount of the stresses that occurs.

Bending of a Cylindrically Aeolotropic Circular Plate With Eccentric Load

1952 ◽  
Vol 19 (1) ◽  
pp. 9-12
Author(s):  
A. M. Sen Gupta
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Uniform Thickness ◽  
Eccentric Load ◽  
Concentrated Load ◽  
Different Boundary Conditions ◽  
Small Deflection ◽  
Deflection Theory ◽  
Clamped Edge

Abstract The problem of small-deflection theory applicable to plates of cylindrically aeolotropic material has been developed, and expressions for moments and deflections produced have been found by Carrier in some symmetrical cases under uniform lateral loadings and with different boundary conditions. The author has also found the moments and deflection in the case of an unsymmetrical bending of a plate loaded by a distribution of pressure of the form p = p0r cos θ, with clamped edge. The object of the present paper is to investigate the problem of the bending of a cylindrically aeolotropic circular plate of uniform thickness under a concentrated load P applied at a point A at a distance b from the center, the edge being clamped.

scholarly journals Parametric study of the effect of phase anisotropy on the micromechanical behaviour of dentin–adhesive interfaces

2005 ◽  
Vol 2 (3) ◽  
pp. 145-157 ◽  
Author(s):  
Anil Misra ◽  
Paulette Spencer ◽  
Orestes Marangos ◽  
Yong Wang ◽  
J. Lawrence Katz
Keyword(s):  
Parametric Study ◽  
Acoustic Microscopy ◽  
Fe Model ◽  
Stress Distributions ◽  
Stress Concentrations ◽  
Hybrid Layer ◽  
Micro Scale ◽  
Failure Initiation ◽  
Interface Phases ◽  
Dentin Adhesive

A finite element (FE) model has been developed based upon the recently measured micro-scale morphological, chemical and mechanical properties of dentin–adhesive (d–a) interfaces using confocal Raman microspectroscopy and scanning acoustic microscopy (SAM). The results computed from this FE model indicated that the stress distributions and concentrations are affected by the micro-scale elastic properties of various phases composing the d–a interface. However, these computations were performed assuming isotropic material properties for the d–a interface. The d–a interface components, such as the peritubular and intertubular dentin, the partially demineralized dentin and the so-called ‘hybrid layer’ adhesive-collagen composite, are probably anisotropic. In this paper, the FE model is extended to account for the probable anisotropic properties of these d–a interface phases. A parametric study is performed to study the effect of anisotropy on the micromechanical stress distributions in the hybrid layer and the peritubular dentin phases of the d–a interface. It is found that the anisotropy of the phases affects the region and extent of stress concentration as well as the location of the maximum stress concentrations. Thus, the anisotropy of the phases could effect the probable location of failure initiation, whether in the peritubular region or in the hybrid layer.

The Design Tradeoffs of Linear Functionally Graded Piezoceramic Actuators

Aerospace ◽  
2003 ◽  
Author(s):  
Paul W. Alexander ◽  
Diann Brei
Keyword(s):  
Material Properties ◽  
High Stress ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Stress Concentrations ◽  
Practical Applications ◽  
Complex Electric Field ◽  
Design Tradeoffs ◽  
A Minor ◽  
The Cost

It is common practice to reduce the voltage level within piezoelectric actuators by utilizing multiple layers, typically bonded together. Unfortunately, this has a tendency to result in device failure due to delamination. For example, with benders the typical lifetime is 105 to 106 cycles, limiting its use in practical applications. This poses an interesting design tradeoff: the stroke is increased due to sharper gradients between material layers; however, the higher gradients lead to high stress concentrations at those interfaces. One approach to reducing these stresses is to grade the material properties through a monolithic piece of piezoceramic so that no interfaces or bonding elements exist, but this comes at the cost of stroke. This paper explores the design tradeoff inherent to monolithic functionally graded piezoelectrics. An analytical free-displacement model for a monolithic piezoceramic beam with a generic gradient is derived. Key to this is the inclusion of the complex electric field distribution which rises from the non-homogeneous material properties. This model is used along with finite element models to examine the effect of continuous linear and stepwise material gradients on the displacement performance as well as the stress levels. The study shows that using monolithic functionally graded piezocermics can significantly reduce the stresses with only a minor impact on the device stroke.

scholarly journals Effect of Fiber Posts on Stress Distribution of Endodontically Treated Upper Premolars: Finite Element Analysis

Nanomaterials ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 1708 ◽  
Author(s):  
Maciej Zarow ◽  
Mirco Vadini ◽  
Agnieszka Chojnacka-Brozek ◽  
Katarzyna Szczeklik ◽  
Grzegorz Milewski ◽  
...  
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Resin Composite ◽  
Von Mises Stress ◽  
Stress Distributions ◽  
Stress Concentrations ◽  
Element Analysis ◽  
Endodontically Treated Tooth ◽  
Maxillary Premolars ◽  
Von Mises

By means of a finite element method (FEM), the present study evaluated the effect of fiber post (FP) placement on the stress distribution occurring in endodontically treated upper first premolars (UFPs) with mesial–occlusal–distal (MOD) nanohybrid composite restorations under subcritical static load. FEM models were created to simulate four different clinical situations involving endodontically treated UFPs with MOD cavities restored with one of the following: composite resin; composite and one FP in the palatal root; composite and one FP in the buccal root; or composite and two FPs. As control, the model of an intact UFP was included. A simulated load of 150 N was applied. Stress distribution was observed on each model surface, on the mid buccal–palatal plane, and on two horizontal planes (at cervical and root-furcation levels); the maximum Von Mises stress values were calculated. All analyses were replicated three times, using the mechanical parameters from three different nanohybrid resin composite restorative materials. In the presence of FPs, the maximum stress values recorded on dentin (in cervical and root-furcation areas) appeared slightly reduced, compared to the endodontically treated tooth restored with no post; in the same areas, the overall Von Mises maps revealed more favorable stress distributions. FPs in maxillary premolars with MOD cavities can lead to a positive redistribution of potentially dangerous stress concentrations away from the cervical and the root-furcation dentin.

scholarly journals Creep-Ductility of High Temperature Steels: A Review

Metals ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 342 ◽  
Author(s):  
Stuart Holdsworth
Keyword(s):  
High Temperature ◽  
Complex Nature ◽  
Stress Concentrations ◽  
Creep Ductility ◽  
Practical Applications ◽  
Long Duration ◽  
Uniaxial Creep ◽  
Modelling Techniques ◽  
Multiaxial Creep

A number of measures of the creep-ductility of high temperature steels are reviewed with an ultimate focus on intrinsic creep-ductility. It is assumed that there will be a future requirement for the determination of long duration creep ductility values for design and product standards in the same way as there is currently for creep strength values. The determination of such information will require specialist modelling techniques to be applied to the complex nature of multi-temperature, multi-heat (multi-cast) data collations, and possible solutions are considered. In service, the exhaustion of creep-ductility is most likely to occur at stress concentrations, and for this, a knowledge of the multiaxial creep-ductility is required, and its relationship to uniaxial creep-ductility. Some practical applications requiring a knowledge of creep-ductility are reviewed.

On Free Vibrations of a Thin Spinning Disk Stiffened With an Outer Reinforcing Ring

1988 ◽  
Vol 110 (4) ◽  
pp. 507-514 ◽  
Author(s):  
S. K. Sinha
Keyword(s):  
Data Storage ◽  
Free Vibrations ◽  
Circular Ring ◽  
Outer Edge ◽  
Design Parameters ◽  
Computer Data ◽  
Storage Devices ◽  
Small Deflection ◽  
Deflection Theory ◽  
Annular Disks

Thin spinning annular disks, which have widely varying applications ranging from inertial wheels in spacecraft to computer data storage devices, experience some inherent vibration problems during operation. One of the techniques to control the vibrations of the disk, being analyzed in this paper, is to stiffen it by attaching a reinforcing ring at its outer edge. The present work considers the effect of adding such a ring and discusses the changes in the natural frequencies for a large range of design parameters. The classical plate bending equation based upon small deflection theory which includes the contribution of rotational membrane stresses has been used in the eigenvalue formulation. Numerical results presented in a nondimensional form should be useful in predicting the dynamic response of such a disk stiffened with a circular ring under the spinning conditions.

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