Higher order stress terms in sharp notch problems under pure‐out‐of‐plane loading

2021 ◽  
Author(s):  
Mohammad R. Mehraban ◽  
Majid R. Ayatollahi ◽  
Bahador Bahrami ◽  
Filippo Berto
Keyword(s):  
Higher Order ◽  
Sharp Notch ◽  
Out Of Plane ◽  
Order Stress

Equivalence Between Higher-Order Stress Power and Heat Flux in Energy Equation Based on Lattice Dynamics

1999 ◽  
Vol 121 (2) ◽  
pp. 240-246 ◽  
Author(s):  
Y. Yasui ◽  
K. Shizawa ◽  
K. Takahashi
Keyword(s):  
Heat Flux ◽  
Lattice Dynamics ◽  
Energy Equation ◽  
Solid Mechanics ◽  
Higher Order ◽  
First Law Of Thermodynamics ◽  
Internal Forces ◽  
Order Stress ◽  
As Stress

The essence of macroscopic quantities in solid mechanics can be grasped by expressing these quantities in terms of kinematic and mechanical quantities of atoms. In this paper, a method is proposed for obtaining the microscopic definitions of internal forces of continua such as stress, higher-order stresses and heat flux. Moreover, the relation between higher-order stress power and heat flux is discussed expressing the first law of thermodynamics with microscopic quantities in the mesodomain. Comparing heat flux with higher-order stress power, it is clarified that the divergence of heat flux is equivalent to the total of each order power due to higher-order stresses.

Analytical Solutions for Crack-Tip Higher Order Stress Fields in Thermal Barrier Coating

2008 ◽  
Vol 47-50 ◽  
pp. 1023-1026
Author(s):  
Yao Dai ◽  
Chang Qing Sun ◽  
Sun Qi ◽  
Wei Tan
Keyword(s):  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Stress Fields ◽  
Thermal Barrier ◽  
Barrier Coating ◽  
Graded Material ◽  
Stress Functions ◽  
Order Stress ◽  
Analytical Expressions

Analytical expressions for crack-tip higher order stress functions for a plane crack in a special functionally graded material (FGM), which has an variation of elastic modulus in 1 2 power form along the gradient direction, are obtained through an asymptotic analysis. The Poisson’s ratio of the FGM is assumed to be constant in the analysis. The higher order fields in the asymptotic expansion display the influence of non-homogeneity on the structure of crack-tip fields obviously. Furthermore, it can be seen from expressions of higher order stress fields that at least three terms must be considered in the case of FGMs in order to explicitly account for non-homogeneity effects on the crack- tip stress fields. These results provide the basis for fracture analysis and engineering applications of this FGM.

Localized Deformation Using Higher Order Stress/Strain Theory

1990 ◽  
Vol 112 (1) ◽  
pp. 51-53 ◽  
Author(s):  
M. A. Koenders
Keyword(s):  
Slip Band ◽  
Failure Modes ◽  
Tangential Force ◽  
Higher Order ◽  
Strain Theory ◽  
Granular Soils ◽  
Localized Deformation ◽  
Contact Points ◽  
Force Ratio ◽  
Order Stress

A material is considered which consists of rough interacting blocks. The interaction, which is expressed in terms of the ratio of the normal and tangential force at the contact points of the blocks, is pure frictional if a certain maximal force ratio is reached, and elastic otherwise. The shape of the blocks is determined by the double shearing geometry. Failure modes for this material depend on the thickness of the slip band. The investigation is relevant to granular soils and rocks.

scholarly journals Influence of in-Plane Deformation in Higher Order Beam Theories

2018 ◽  
Vol 68 (3) ◽  
pp. 77-94 ◽  
Author(s):  
Evangelos Sapountzakis ◽  
Amalia Argyridi
Keyword(s):  
Degrees Of Freedom ◽  
Plane Deformation ◽  
Beam Theory ◽  
Higher Order ◽  
Essential Difference ◽  
Numerical Example ◽  
Out Of Plane ◽  
Geometric Constants ◽  
Beam Theories

AbstractComparing Euler-Bernoulli or Tismoshenko beam theory to higher order beam theories, an essential difference can be depicted: the additional degrees of freedom accounting for out-of plane (warping) and in-plane (distortional) phenomena leading to the appearance of respective higher order geometric constants. In this paper, after briefly overviewing literature of the major beam theories taking account warping and distortional deformation, the influence of distortion in the response of beams evaluated by higher order beam theories is examined via a numerical example of buckling drawn from the literature.

Higher-order ferromagnetic resonances in out-of-plane saturated Co/Au magnetic multilayers

2020 ◽  
Vol 102 (9) ◽  
Author(s):  
L. Fallarino ◽  
S. Stienen ◽  
R. A. Gallardo ◽  
J. A. Arregi ◽  
V. Uhlíř ◽  
...  
Keyword(s):  
Magnetic Multilayers ◽  
Higher Order ◽  
Out Of Plane

A Survey With Numerical Assessment of Classical and Refined Theories for the Analysis of Sandwich Plates

2008 ◽  
Vol 62 (1) ◽  
Author(s):  
E. Carrera ◽  
S. Brischetto
Keyword(s):  
Higher Order ◽  
Benchmark Problems ◽  
Geometrical Parameters ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Numerical Assessment ◽  
Shell Analysis ◽  
Out Of Plane ◽  
The Face ◽  
Free Vibration Response

A large variety of plate theories are described and assessed in the present work to evaluate the bending and vibration of sandwich structures. A brief survey of available works is first given. Such a survey includes significant review papers and latest developments on sandwich structure modelings. The kinematics of classical, higher order, zigzag, layerwise, and mixed theories is described. An exhaustive numerical assessment of the whole theories is provided in the case of closed form solutions of simply supported panels made of orthotropic layers. Reference is made to the unified formulation that has recently been introduced by the first author for a plate/shell analysis. Attention has been given to displacements, stresses (both in-plane and out-of-plane components), and the free vibration response. Only simply supported orthotropic panels loaded by a transverse distribution of bisinusoidal pressure have been analyzed. Five benchmark problems are treated. The accuracy of the plate theories is established with respect to the length-to-thickness-ratio (LTR) geometrical parameters and to the face-to-core-stiffness-ratio (FCSR) mechanical parameters. Two main sources of error are outlined, which are related to LTR and FCSR, respectively. It has been concluded that higher order theories (HOTs) can be conveniently used to reduce the error due to LTR in thick plate cases. But HOTs are not effective in increasing the accuracy of the classical theory analysis whenever the error is caused by increasing FCSR values; layerwise analysis becomes mandatory in this case.

A higher-order stress-based gradient-enhanced damage model based on isogeometric analysis

2016 ◽  
Vol 304 ◽  
pp. 584-604 ◽  
Author(s):  
Tran Quoc Thai ◽  
Timon Rabczuk ◽  
Yuri Bazilevs ◽  
Günther Meschke
Keyword(s):  
Isogeometric Analysis ◽  
Damage Model ◽  
Higher Order ◽  
Model Based ◽  
Order Stress

Exact Matching Condition at a Joint of Thin-Walled Box Beams Under Out-of-Plane Bending and Torsion

2012 ◽  
Vol 79 (5) ◽  
Author(s):  
Soomin Choi ◽  
Gang-Won Jang ◽  
Yoon Young Kim
Keyword(s):  
Beam Theory ◽  
Matching Condition ◽  
Higher Order ◽  
Transformation Matrix ◽  
Exact Matching ◽  
Box Beam ◽  
Out Of Plane ◽  
Box Beams ◽  
Thin Walled ◽  
Plane Bending

To take into account the flexibility resulting from sectional deformations of a thin-walled box beam, higher-order beam theories considering warping and distortional degrees of freedom (DOF) in addition to the Timoshenko kinematic degrees have been developed. The objective of this study is to derive the exact matching condition consistent with a 5-DOF higher-order beam theory at a joint of thin-walled box beams under out-of-plane bending and torsion. Here we use bending deflection, bending/shear rotation, torsional rotation, warping, and distortion as the kinematic variables. Because the theory involves warping and distortion that do not produce any force/moment resultant, the joint matching condition cannot be obtained just by using the typical three equilibrium conditions. This difficulty poses considerable challenges because all elements of the 5×5 transformation matrix relating the field variables of one beam to those in another beam should be determined. The main contributions of the investigation are to propose additional necessary conditions to determine the matrix and to derive it exactly. The validity of the derived joint matching transformation matrix is demonstrated by showing good agreement between the shell finite element results and those obtained by the present box beam analysis in various angle box beams.

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