Composite Laminate Stiffnesses and Their Sensitivities

1994 ◽  
Author(s):  
Bodo Geier ◽  
Rolf Zimmermann
Keyword(s):  
Composite Materials ◽  
Transverse Shear ◽  
Composite Laminate ◽  
Shear Stiffness ◽  
Efficient Algorithms ◽  
Search Procedure ◽  
Object Function ◽  
Stiffness Matrices ◽  
Derivatives Of ◽  
Constrained Function

Abstract The great number of possible stacking orders to form laminates suggests to apply optimization, more frequently than usual, in the design of structures made of composite materials. One of the columns upon which optimization of structures is built is the mathematical search procedure for locating a minimum (or maximum) of a constrained function. Efficient algorithms will require the evaluation of derivatives of the object function as well as of the constraints. In that context the sensitivities of laminate stiffness matrices may be required. In order to meet such a requirement the derivatives with respect to both ply thicknesses and ply angles, of laminate stiffnesses, including transverse shear stiffness, will be presented in this report.

scholarly journals Determination of Transverse Shear Stiffness of Sandwich Panels with a Corrugated Core by Numerical Homogenization

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1976
Author(s):  
Tomasz Garbowski ◽  
Tomasz Gajewski
Keyword(s):  
Transverse Shear ◽  
Shear Stiffness ◽  
The Finite Element Method ◽  
Homogenization Procedure ◽  
Plate Structures ◽  
Corrugated Board ◽  
Energy Equivalence ◽  
The Stability ◽  
Global Stiffness Matrix

Knowing the material properties of individual layers of the corrugated plate structures and the geometry of its cross-section, the effective material parameters of the equivalent plate can be calculated. This can be problematic, especially if the transverse shear stiffness is also necessary for the correct description of the equivalent plate performance. In this work, the method proposed by Biancolini is extended to include the possibility of determining, apart from the tensile and flexural stiffnesses, also the transverse shear stiffness of the homogenized corrugated board. The method is based on the strain energy equivalence between the full numerical 3D model of the corrugated board and its Reissner-Mindlin flat plate representation. Shell finite elements were used in this study to accurately reflect the geometry of the corrugated board. In the method presented here, the finite element method is only used to compose the initial global stiffness matrix, which is then condensed and directly used in the homogenization procedure. The stability of the proposed method was tested for different variants of the selected representative volume elements. The obtained results are consistent with other technique already presented in the literature.

A C0 three-node triangular element based on preprocessing approach for thick sandwich plates

2017 ◽  
Vol 21 (6) ◽  
pp. 1820-1842
Author(s):  
Wu Zhen ◽  
Ma Rui ◽  
Chen Wanji
Keyword(s):  
Transverse Shear ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Higher Order ◽  
Triangular Element ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Transverse Shear Stress ◽  
Transverse Shear Stresses ◽  
Derivatives Of

This paper will try to overcome two difficulties encountered by the C0 three-node triangular element based on the displacement-based higher-order models. They are (i) transverse shear stresses computed from constitutive equations vanish at the clamped edges, and (ii) it is difficult to accurately produce the transverse shear stresses even using the integration of the three-dimensional equilibrium equation. Invalidation of the equilibrium equation approach ought to attribute to the higher-order derivations of displacement parameters involved in transverse shear stress components after integrating three-dimensional equilibrium equation. Thus, the higher-order derivatives of displacement parameters will be taken out from transverse shear stress field by using the three-field Hu–Washizu variational principle before the finite element procedure is implemented. Therefore, such method is named as the preprocessing method for transverse shear stresses in present work. Because the higher-order derivatives of displacement parameters have been eliminated, a C0 three-node triangular element based on the higher-order zig-zag theory can be presented by using the linear interpolation function. Performance of the proposed element is numerically evaluated by analyzing multilayered sandwich plates with different loading conditions, lamination sequences, material constants and boundary conditions, and it can be found that the present model works well in the finite element framework.

Transverse shear stiffness of structural core sandwich

1994 ◽  
Vol 27 (3) ◽  
pp. 317-329 ◽  
Author(s):  
Tomas Nordstrand ◽  
Leif A. Carlsson ◽  
Howard G. Allen
Keyword(s):  
Transverse Shear ◽  
Shear Stiffness

Dynamic Behavior of Aircraft Wings Modeled as Doubly-Tapered Composite Thin-Walled Beams

1999 ◽  
Author(s):  
Sungsoo Na ◽  
Liviu Librescu
Keyword(s):  
Composite Materials ◽  
Free Vibration ◽  
Dynamic Response ◽  
Dynamic Behavior ◽  
Transverse Shear ◽  
Dynamical Behavior ◽  
Time Dependent ◽  
Aircraft Wings ◽  
Helicopter Blades ◽  
Thin Walled

Abstract A study of the dynamical behavior of aircraft wings modeled as doubly-tapered thin-walled beams, made from advanced anisotropic composite materials, and incorporating a number of non-classical effects such as transverse shear, and warping inhibition is presented. The supplied numerical results illustrate the effects played by the taper ratio, anisotropy of constituent materials, transverse shear flexibility, and warping inhibition on free vibration and dynamic response to time-dependent external excitations. Although considered for aircraft wings, this analysis and results can be also applied to a large number of structures such as helicopter blades, robotic manipulator arms, space booms, tall cantilever chimneys, etc.

scholarly journals Factors contributing to the transverse shear stiffness of bolted cold-formed steel storage rack upright frames with channel bracing members

2019 ◽  
Vol 136 ◽  
pp. 50-63 ◽  
Author(s):  
Nima Talebian ◽  
Benoit P. Gilbert ◽  
Nadia Baldassino ◽  
Hassan Karampour
Keyword(s):  
Transverse Shear ◽  
Shear Stiffness ◽  
Cold Formed Steel

scholarly journals Determining the transverse shear stiffness of steel storage rack upright frames

2012 ◽  
Vol 78 ◽  
pp. 107-116 ◽  
Author(s):  
Benoit P. Gilbert ◽  
Kim J.R. Rasmussen ◽  
Nadia Baldassino ◽  
Tito Cudini ◽  
Leo Rovere
Keyword(s):  
Transverse Shear ◽  
Shear Stiffness

scholarly journals Experimental Study on Vertical Shear Behaviors of an Immersion Joint with Steel Shear Keys

2019 ◽  
Vol 9 (23) ◽  
pp. 5056
Author(s):  
Yong Yuan ◽  
Jianhui Luo ◽  
Haitao Yu
Keyword(s):  
Transverse Shear ◽  
Shear Test ◽  
Compressive Load ◽  
Shear Stiffness ◽  
Development Stage ◽  
Shear Capacity ◽  
Vertical Shear ◽  
Shear Load ◽  
Shear Keys ◽  
Shear Behaviors

The vertical shear behaviors of an immersion joint with steel shear keys subjected to multidirectional loads are investigated in this paper. An experiment of an immersion joint model is carried out. Two kinds of compression–shear tests of the joint are considered in this experiment. The first kind of compression–shear test applies a specific vertical shear load and five different levels of longitudinal compressive loads on the joint. An additional compression–vertical shear destruction test is also conducted under the minimum longitudinal compressive load, wherein the vertical shear load is incrementally increased until failure of the joint. The other kind of compression–shear test is a bidirectional shear test, in which both the longitudinal compressive load and the transverse shear load are fixed, and the vertical shear load is gradually increased until reaching a target value. The results show that the shear force–displacement curves of the joint in any loading case can be divided into two stages: a non-linear development stage and a quasi-linear development stage. The vertical shear stiffness of the joint is found to increase with increasing longitudinal compressive load, and the existence of a transverse shear load enhances this effect. The ultimate shear capacity of the joint is smaller than the sum of the shear capacities of all vertical steel keys. In addition, the failure of the joint appears at the shear key on one sidewall of the joint.

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