scholarly journals Shape functions for high-order shear deformation beam element

2021 ◽  
Author(s):  
Himanshu Gaur ◽  
Mahmoud Dawood ◽  
Ram Kishore Manchiryal
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Beam Theory ◽  
Order Theory ◽  
Beam Element ◽  
High Order ◽  
Shape Functions ◽  
High Order Theory ◽  
Cubic Polynomial ◽  
Transverse Deflection

In this article, shape functions for higher-order shear deformation beam theory are derived. For the two nodded beam element, transverse deflection is assumed as cubic polynomial. By using equations of equilibrium of high-order theory that are already derived by J. N. Reddy in 1997, equation for slope of high- order theory is found. Finally with the boundary conditions of beam element and assumed kinematics of high-order theory, shape functions are derived.

scholarly journals In-plane vibration of rotating rings using a high order theory

2018 ◽  
Vol 211 ◽  
pp. 03012
Author(s):  
Tao Lu ◽  
Apostolos Tsouvalas ◽  
Andrei Metrikine
Keyword(s):  
Boundary Conditions ◽  
Order Theory ◽  
High Order ◽  
Thickness Variation ◽  
Shear Stresses ◽  
Plane Vibration ◽  
High Order Theory ◽  
Inner Surface ◽  
Displacement Pattern ◽  
Tire Dynamics

In-plane dynamics of rotating rings on elastic foundation is a topic of continuous research, especially in the field of tire dynamics. When the inner surface of a ring is connected to a stiff foundation, the through-thickness variation of radial and shear stress needs to be accounted for. This effect is often overlooked in the ring models proposed in the literature. In this paper, a new high order theory is developed for the in-plane vibration of rotating rings whose inner surface is connected to an immovable hub by distributed springs while the outer surface is stress-free. The high-order terms are chosen such that the boundary conditions at the inner and outer surfaces are satisfied at all times. Instability, which is usually overlooked in the literature, is predicted using the present model. Resonant speeds are investigated, at which modes appear as a stationary displacement pattern to a space-fixed observer. The exact satisfaction of boundary conditions at the inner and outer ring surfaces together with the through-thickness variation of the radial and shear stresses are shown to be of significant importance when the ring rotates at high speeds or is supported by relatively stiff foundation.

Delamination analysis of sandwich beam - High-order theory

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 981-986
Author(s):  
F. Minghui ◽  
L. Zuoqiu ◽  
Y. Jiuren
Keyword(s):  
Sandwich Beam ◽  
Order Theory ◽  
High Order ◽  
High Order Theory

A High-Order Theory of Plate Deformation—Part 2: Laminated Plates

1977 ◽  
Vol 44 (4) ◽  
pp. 669-676 ◽  
Author(s):  
K. H. Lo ◽  
R. M. Christensen ◽  
E. M. Wu
Keyword(s):  
Classical Theory ◽  
Present Theory ◽  
Order Theory ◽  
Laminated Plates ◽  
High Order ◽  
Plate Deformation ◽  
High Order Theory ◽  
Elasticity Solutions

The high-order theory of plate deformation developed in Part 1 of this work is extended here to model the behavior of laminated plates. Through comparison with elasticity solutions, it is shown the present theory correctly models effects not attainable from the classical theory.

Delamination Analysis of Sandwich Beam: High-Order Theory

AIAA Journal ◽  
2002 ◽  
Vol 40 (5) ◽  
pp. 981-986 ◽  
Author(s):  
Fu Minghui ◽  
Liu Zuoqiu ◽  
Yin Jiuren
Keyword(s):  
Sandwich Beam ◽  
Order Theory ◽  
High Order ◽  
High Order Theory

A High-Order Theory of Plate Deformation—Part 1: Homogeneous Plates

1977 ◽  
Vol 44 (4) ◽  
pp. 663-668 ◽  
Author(s):  
K. H. Lo ◽  
R. M. Christensen ◽  
E. M. Wu
Keyword(s):  
Lower Order ◽  
Plate Thickness ◽  
Order Theory ◽  
Laminated Plates ◽  
High Order ◽  
Normal Strain ◽  
Plate Deformation ◽  
High Order Theory ◽  
Load Pattern ◽  
Sinusoidal Surface

A theory of plate deformation is derived which accounts for the effects of transverse shear deformation, transverse normal strain, and a nonlinear distribution of the in-plane displacements with respect to the thickness coordinate. The theory is compared with lower-order plate theories through application to a particular problem involving a plate acted upon by a sinusoidal surface pressure. Comparison is also made with the exact elasticity solution of this problem. It is found that when the ratio of the characteristic length of the load pattern to the plate thickness is of the order of unity, lower-order theories are inadequate and the present high-order theory is required to give meaningful results. The present work treats homogeneous plates while Part 2 involves laminated plates.

Research and Applications of a Plane Embedded Combined Element Model Considering Bond and Slip

2013 ◽  
Vol 275-277 ◽  
pp. 1296-1301
Author(s):  
Ji Wei Wang ◽  
Qin Qin Qiao ◽  
Fei Leng
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Shear Deformation ◽  
Element Model ◽  
Beam Element ◽  
Shape Functions ◽  
Element Analysis ◽  
Bond Slip ◽  
Numerical Examples ◽  
Nodal Force

It is one of the most important issues for finite element analysis of lining structures that how to describe anchor rod reasonably and effectively and simulate the interaction between rod and concrete or rock. Virtual nodes are constructed in concrete/rock element at the ends of anchor rod and bond-slip element is set between virtual nodes and beam element which describes anchor rod. An embedded combined element with bond slip and shear deformation is established through the transformation of nodal force at nodes of bond-slip element to those of concrete/rock element via shape functions. The element is convenient for meshing element because the location and direction of anchor rod are not necessary to be considered. Meanwhile, the element has the advantage of low computing cost. Finally, the validity and efficiency are verified by numerical examples.

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