AN IMPROVED METHOD OF CALCULATING BEAM DEFORMATION CONSIDERING TRANSVERSE SHEAR STRAIN

2021 ◽  
Vol 21 (83) ◽  
Author(s):  
Do Thang
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Transverse Shear Strain ◽  
Improved Method

On the nominal transverse shear strain to characterize the severity of creasing

TAPPI Journal ◽  
2018 ◽  
Vol 17 (04) ◽  
pp. 231-240
Author(s):  
Douglas Coffin ◽  
Joel Panek
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Elastic Limit ◽  
Experimental Results ◽  
Transverse Shear Strain ◽  
Maximum Strain ◽  
Machine Direction ◽  
Engineering Approach ◽  
Wide Range ◽  
Analytic Expression

A transverse shear strain was utilized to characterize the severity of creasing for a wide range of tooling configurations. An analytic expression of transverse shear strain, which accounts for tooling geometry, correlated well with relative crease strength and springback as determined from 90° fold tests. The experimental results show a minimum strain (elastic limit) that needs to be exceeded for the relative crease strength to be reduced. The theory predicts a maximum achievable transverse shear strain, which is further limited if the tooling clearance is negative. The elastic limit and maximum strain thus describe the range of interest for effective creasing. In this range, cross direction (CD)-creased samples were more sensitive to creasing than machine direction (MD)-creased samples, but the differences were reduced as the shear strain approached the maximum. The presented development provides the foundation for a quantitative engineering approach to creasing and folding operations.

scholarly journals Investigation of porosity effect on flexural analysis of doubly curved FGM conoids

2019 ◽  
Vol 26 (1) ◽  
pp. 435-448
Author(s):  
Md Irfan Ansari ◽  
Ajay Kumar ◽  
Danuta Barnat-Hunek ◽  
Zbigniew Suchorab ◽  
Bartłomiej Kwiatkowski
Keyword(s):  
Mathematical Model ◽  
Shear Strain ◽  
Transverse Shear ◽  
Volume Fraction ◽  
Current Model ◽  
Lower Surface ◽  
Functionally Graded ◽  
Transverse Shear Strain ◽  
Flexural Analysis ◽  
Doubly Curved

AbstractThe flexural analysis of doubly curved functionally graded porous conoids was performed in the present paper. The porosities inside functionally graded materials (FGMs) can occur during the fabrication and lead to the occurrence of micro-voids in the materials. The mathematical model includes expansion of Taylor’s series up to the third degree in thickness coordinate and normal curvatures in in-plane displacement fields. Since there is a parabolic variation in transverse shear strain deformation across the thickness coordinate, the shear correction factor is not necessary. The condition of zero-transverse shear strain at upper and lower surface of conoidal shell is implemented in the present model. The improvement in the 2D mathematical model enables to solve problems of moderately thick FGM porous conoids. The distinguishing feature of the present shell from the other shells is that maximum transverse deflection does not occur at its centre. The improved mathematical model was implemented in finite element code written in FORTRAN. The obtained numerical results were compared with the results available in the literature. Once validated, the current model was employed to study the effect of porosity, boundary condition, volume fraction index, loading pattern and others geometric parameters.

A Higher-Order Theory for Vibration Analysis of Curvilinear Thick Shallow Shells with Constrained Boundaries

1995 ◽  
Vol 1 (1) ◽  
pp. 15-39 ◽  
Author(s):  
K.M. Liew ◽  
C.W. Lim
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Vibration Analysis ◽  
Numerical Procedure ◽  
Higher Order ◽  
Mode Shapes ◽  
Transverse Shear Strain ◽  
Shallow Shells ◽  
Displacement Mode ◽  
Wide Range

This article presents the vibration analysis of thick doubly curved shallow shells having curvilinear planform. The Gaussian curvature of shell varies from positive (such as spherical) to negative (such as hyperbolic paraboloidal). The boundaries are constrained with either soft-simply supported or fully clamped edges. A higher-order shear deformation theory, which includes transverse shear strain and rotary inertia, is developed to model the vibration characteristics of the shell. The inclusion of Lamé parameters in the present formulation accounts for the presence of shell curvature and yields cubic transverse shear strain distribution in contrast with the existing quadratic expressions. A set of versatile, globally continuous shape functions is adopted in the Ritz numerical procedure to approximate the displacement and rotation fields. A set of new results for a wide range of shell configurations is presented with some selected contour and three-dimensional displacement mode shapes.

On the use of an enhanced transverse shear strain shell element for problems involving large rotations

2003 ◽  
Vol 30 (4) ◽  
pp. 286-296 ◽  
Author(s):  
R. A. Fontes Valente ◽  
R. M. Natal Jorge ◽  
R. P. R. Cardoso ◽  
J. M. A. C�sar de S� ◽  
J. J. A. Gr�cio
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Shell Element ◽  
Transverse Shear Strain ◽  
Large Rotations

Creasing severity and reverse-side cracking

TAPPI Journal ◽  
2020 ◽  
Vol 19 (4) ◽  
pp. 219-227
Author(s):  
JOEL C. PANEK ◽  
SWAN D. SMITH ◽  
DOUGLAS W. COFFIN
Keyword(s):  
Shear Strain ◽  
Penetration Depth ◽  
Transverse Shear ◽  
System Parameter ◽  
Transverse Shear Strain ◽  
Material System ◽  
Critical Depth ◽  
Penetration Depths ◽  
Severity Parameter ◽  
Channel Combination

Crease cracking can be detrimental to the functionality and appearance of paperboard-based pack-aging. The effect of creasing severity on the degree of reverse-side crease cracking (bead-side of the crease) of paperboard was investigated. Samples were creased with a range of rule and channel geometries, and the cracking degree was quantified as the percent of cracked length relative to the total length of the crease. The cracking degree was typically below 5% at low crease penetration depths, but was exponentially higher beyond a critical penetration depth. A rule and channel combination with a wider clearance shifted the critical depth to larger values. The creasing severity parameter, termed the creasing draw, converged the cracking degree data from different rule and channel combinations to a single curve. The creasing draw was derived from the same analytical expres-sions as the transverse shear strain and quantifies the length of paper that is drawn into the channel during creasing. The critical draw is defined as the draw at which cracking becomes greater than 5%, which corresponds with the point at which cracking becomes exponential. The critical draw is a material/system parameter that defines the level below which cracking is minimal.

Analysis of shear flexible beams, using the meshless local Petrov‐Galerkin method, based on a locking‐free formulation

2001 ◽  
Vol 18 (1/2) ◽  
pp. 215-240 ◽  
Author(s):  
J.Y. Cho ◽  
S.N. Atluri
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Weak Form ◽  
Transverse Displacement ◽  
Transverse Shear Strain ◽  
Weak Formulation ◽  
Flexible Beams ◽  
Thin Beam ◽  
Dependent Variables ◽  
Mlpg Method

The problems of shear flexible beams are analyzed by the MLPG method based on a locking‐free weak formulation. In order for the weak formulation to be locking‐free, the numerical characteristics of the variational functional for a shear flexible beam, in the thin beam limit, are discussed. Based on these discussions a locking‐free local symmetric weak form is derived by changing the set of two dependent variables in governing equations from that of transverse displacement and total rotation to the set of transverse displacement and transverse shear strain. For the interpolation of the chosen set of dependent variables (i.e. transverse displacement and transverse shear strain) in the locking‐free local symmetric weak form, the recently proposed generalized moving least squares (GMLS) interpolation scheme is utilized, in order to introduce the derivative of the transverse displacement as an additional nodal degree of freedom, independent of the nodal transverse displacement. Through numerical examples, convergence tests are performed. To identify the locking‐free nature of the proposed method, problems of shear flexible beams in the thick beam limit and in the thin beam limit are analyzed, and the numerical results are compared with analytical solutions. The potential of using the truly meshless local Petrov‐Galerkin (MLPG) method is established as a new paradigm in totally locking‐free computational analyses of shear flexible plates and shells.

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