scholarly journals An Elastic Interface Model for the Delamination of Bending-Extension Coupled Laminates

2019 ◽  
Vol 9 (17) ◽  
pp. 3560 ◽  
Author(s):  
Stefano Bennati ◽  
Paolo Fisicaro ◽  
Luca Taglialegne ◽  
Paolo Valvo
Keyword(s):  
Mathematical Problem ◽  
Interfacial Crack ◽  
Laminated Beam ◽  
Generalized Displacements ◽  
Elastic Interface ◽  
Internal Forces ◽  
Crack Tip Element ◽  
Double Cantilever Beam Test ◽  
Strain Measures ◽  
Shear Deformable

The paper addresses the problem of an interfacial crack in a multi-directional laminated beam with possible bending-extension coupling. A crack-tip element is considered as an assemblage of two sublaminates connected by an elastic-brittle interface of negligible thickness. Each sublaminate is modeled as an extensible, flexible, and shear-deformable laminated beam. The mathematical problem is reduced to a set of two differential equations in the interfacial stresses. Explicit expressions are derived for the internal forces, strain measures, and generalized displacements in the sublaminates. Then, the energy release rate and its Mode I and Mode II contributions are evaluated. As an example, the model is applied to the analysis of the double cantilever beam test with both symmetric and asymmetric laminated specimens.

Split Rigidity Method for Analysis of Three-Way Double-Layer Space Grids Structure

2012 ◽  
Vol 594-597 ◽  
pp. 820-823
Author(s):  
Wen Yang Liu ◽  
Wen Fu Zhang
Keyword(s):  
Double Layer ◽  
Natural Vibration ◽  
Sandwich Plate ◽  
High Accuracy ◽  
Traditional Theory ◽  
Natural Vibration Frequency ◽  
Plate Method ◽  
Generalized Displacements ◽  
Internal Forces ◽  
Shearing Deformation

Abstract. In this paper three-way double-layer space grids structure is assumed as equivalent sandwich plate, and has been analyzed by the non-traditional theory of plate with three generalized displacements, in which shearing deformation is considered. Based upon the split rigidity method, static analysis and natural vibration analysis of three-way double-layer space grids structure has been studied. The formulas for calculating internal forces, displacement as well as natural vibration frequency are given out. The comparison with finite element method and equivalent sandwich plate method shows that the formulas in this paper are not only simpler than other simplified methods but also of high accuracy.

Isogeometric boundary integral formulation for Reissner’s plate problems

2019 ◽  
Vol 37 (1) ◽  
pp. 21-53
Author(s):  
Ahmed K. Abdelmoety ◽  
Taha H.A. Naga ◽  
Youssef F. Rashed
Keyword(s):  
Singular Integrals ◽  
Boundary Integral ◽  
Element Formulation ◽  
Analysis Tool ◽  
Content Type ◽  
Nurbs Curves ◽  
Generalized Displacements ◽  
Spline Basis ◽  
Shear Deformable ◽  
Shear Deformable Plates

Purpose This paper aims to develop a new isogeometric boundary element formulation based on non-uniform rational basis splines (NURBS) curves for solving Reissner’s shear-deformable plates. Design/methodology/approach The generalized displacements and tractions along the problem boundary are approximated as NURBS curves having the same rational B-spline basis functions used to describe the geometrical boundary of the problem. The source points positions are determined over the problem boundary by the well-known Greville abscissae definition. The singular integrals are accurately evaluated using the singularity subtraction technique. Findings Numerical examples are solved to demonstrate the validity and the accuracy of the developed formulation. Originality/value This formulation is considered to preserve the exact geometry of the problem and to reduce or cancel mesh generation time by using NURBS curves employed in computer aided designs as a tool for isogeometric analysis. The present formulation extends such curves to be implemented as a stress analysis tool.

Transient Stress Intensity Factors of an Interfacial Crack Between Two Dissimilar Anisotropic Half-Spaces, Part 2: Fully Anisotropic Materials

1984 ◽  
Vol 51 (4) ◽  
pp. 780-786 ◽  
Author(s):  
A.-Y. Kuo
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Jacobi Polynomials ◽  
Mathematical Problem ◽  
Stress Singularity ◽  
Interfacial Crack ◽  
Singular Integral Equations ◽  
Intensity Factors

Dynamic stress intensity factors for an interfacial crack between two dissimilar elastic, fully anisotropic media are studied. The mathematical problem is reduced to three coupled singular integral equations. Using Jacobi polynomials, solutions to the singular integral equations are obtained numerically. The orders of stress singularity and stress intensity factors of an interfacial crack in a (θ(1)/θ(2)) composite solid agree well with the finite element solutions.

Split Rigidity Method for Analysis of Double-Layer Space Grids Structure with Rectangular Shape

2012 ◽  
Vol 446-449 ◽  
pp. 480-483
Author(s):  
Wen Yang Liu ◽  
Wen Fu Zhang
Keyword(s):  
Double Layer ◽  
Natural Vibration ◽  
Sandwich Plate ◽  
High Accuracy ◽  
Traditional Theory ◽  
Plate Method ◽  
Rectangular Shape ◽  
Generalized Displacements ◽  
Internal Forces ◽  
Shearing Deformation

In this paper double-layer space grids structure with rectangular shape is assumed as equivalent sandwich plate, and has been analyzed by the non-traditional theory of plate with three generalized displacements, in which shearing deformation is considered. Based upon the split rigidity method, static analysis and natural vibration analysis of double-layer space grids structure has been studied. The formulas for calculating internal forces, displacement as well as fundamental frequency are given out. The comparison with finite element method and equivalent sandwich plate method shows that split rigidity method is not only simpler than other simplified methods but also of high accuracy.

On Flexural Vibrations of Shear Deformable Laminated Beams

2012 ◽  
Author(s):  
Stefano Lenci ◽  
Francesco Clementi
Keyword(s):  
Mechanical Characteristics ◽  
Natural Frequencies ◽  
Normal Direction ◽  
Rotational Inertia ◽  
Shear Deformations ◽  
Various Boundary Conditions ◽  
Elastic Interface ◽  
Shear Deformable ◽  
Perfect Adherence ◽  
Tangential Directions

The natural frequencies of a two-layer beam with an elastic interface are investigated. Each beam is modeled by the Timoshenko kinematics, and the interface coupling is linear in both normal and tangential directions. Attention is focused on the shear deformation, axial and rotational inertia, and interface normal stiffness. The dependence of the natural frequencies on these mechanical characteristics is investigated by solving the associated eigenvalue problem. The convergence of the solution toward that of a simplified problem obtained by neglecting axial and rotational inertia, shear deformations and by considering interface perfect adherence in the normal direction, is studied. Various boundary conditions are investigated to extend the generality of the proposed results.

A control algorithm for nonlinear offshore structural dynamical systems

2015 ◽  
Vol 471 (2184) ◽  
pp. 20150605 ◽  
Author(s):  
R. Manikandan ◽  
Nilanjan Saha
Keyword(s):  
Control Algorithm ◽  
Control Mechanism ◽  
Full Rank ◽  
Control Law ◽  
Structural Systems ◽  
Environmental Loads ◽  
State Dependent ◽  
Generalized Displacements ◽  
Internal Forces ◽  
Nonlinear Motions

A reasonable knowledge about the response of nonlinear offshore structural systems under environmental loads is necessary but challenging. This is due to the coupling of internal forces along with external excitations. In this paper, a mathematical model of nonlinear offshore systems is studied with the intention of keeping the response close to the desired one. This is achieved using a novel sub-optimal control mechanism derived from nonlinear quadratic regulator (NQR) theory. Herein, two linearized functions of nonlinear motions—displacement and velocity—are introduced such that the parametrization of the state-dependent system matrices is obtained. By doing so, the system becomes conditioned only on the present state and therefore one needs to solve only an algebraic state-dependent Riccati problem. This results in a control law which may either be partial or full rank for the dynamical system depending on measurable states. The performance of the controller is compared with conventional NQR. The performance of the proposed control strategy is illustrated through a range of models of nonlinear offshore problems. The motions (generalized displacements and velocities) show that the proposed controller was not only able to restrict the undesirable behaviour but also provide means of shaping the transient performance.

A Sixth-Order Theory of Shear Deformable Beams With Variational Consistent Boundary Conditions

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Guangyu Shi ◽  
George Z. Voyiadjis
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Cross Sections ◽  
Beam Theory ◽  
Order Theory ◽  
Sixth Order ◽  
Equilibrium Equations ◽  
Flexible Beams ◽  
Generalized Displacements ◽  
Shear Deformable

This paper presents the derivation of a new beam theory with the sixth-order differential equilibrium equations for the analysis of shear deformable beams. A sixth-order beam theory is desirable since the displacement constraints of some typical shear flexible beams clearly indicate that the boundary conditions corresponding to these constraints can be properly satisfied only by the boundary conditions associated with the sixth-order differential equilibrium equations as opposed to the fourth-order equilibrium equations in Timoshenko beam theory. The present beam theory is composed of three parts: the simple third-order kinematics of displacements reduced from the higher-order displacement field derived previously by the authors, a system of sixth-order differential equilibrium equations in terms of two generalized displacements w and ϕx of beam cross sections, and three boundary conditions at each end of shear deformable beams. A technique for the analytical solution of the new beam theory is also presented. To demonstrate the advantages and accuracy of the new sixth-order beam theory for the analysis of shear flexible beams, the proposed beam theory is applied to solve analytically three classical beam bending problems to which the fourth-order beam theory of Timoshenko has created some questions on the boundary conditions. The present solutions of these examples agree well with the elasticity solutions, and in particular they also show that the present sixth-order beam theory is capable of characterizing some boundary layer behavior near the beam ends or loading points.

scholarly journals Correction force for releasing crack tip element with XFEM and only discontinuous enrichment

2009 ◽  
pp. 465-483
Author(s):  
Thomas Menouillard ◽  
Ted Belytschko
Keyword(s):  
Finite Element Method ◽  
Extended Finite Element Method ◽  
Crack Tip ◽  
Stress Waves ◽  
Intensity Factors ◽  
Extended Finite Element ◽  
Binary Description ◽  
Discontinuous Enrichment ◽  
Internal Forces ◽  
Crack Tip Element

This paper deals with numerical crack propagation and makes use of the extended finite element method in the case of explicit dynamics. The advantage of this method is the absence of remeshing. The use of XFEM with Heaviside functions only gives a binary description of the crack tip element: cut or not. Here, we modify the internal forces with a correction force in order to smoothly release the tip element while the virtual crack tip travels through an element. This avoids creating non physical stress waves and improves the accuracy of the evaluation of the stress intensity factors during propagation.

scholarly journals A Mathematical Model of the Strain and Stress Kinetics during Welding of Thin-Walled Products

2018 ◽  
Vol 249 ◽  
pp. 02005
Author(s):  
Gocha Gubeladze ◽  
Paata Geradze
Keyword(s):  
Mathematical Model ◽  
Three Dimensional ◽  
Generalized Displacements ◽  
Internal Forces ◽  
Linear Version ◽  
Thin Walled ◽  
Stress States ◽  
Basic Equations ◽  
Thermal Phenomena ◽  
Theory Of Shells

The paper dwells on the mathematical model of the strain and stress of the elements of the thin-walled systems. A version of the sophisticated theory of shells with the use of several base surfaces has been developed at the Kutaisi Technical University [3,8]. The theory is based on a kinematic hypothesis thereby facilitating the construction of a three-dimensional field of deformation of shell by deformation of two or more surfaces. The use of several base surfaces allows not only for accounting the transverse shears and crimping, but also, with account for the shell thickness, for modeling the mechanical and thermal phenomena on the front surfaces of the layers. In doing so, the geometrical and mechanistic interpretation of generalized displacements and generalized internal forces is clear enough, and the basic equations are simple. The model is based on a geometrically linear version of the theory of shells with the use of several base surfaces and the theory of non-isothermal plastic flow [4]. The developed mathematical model of the strain and stress kinetics allows for evaluating the temperature and strain-stress states of thin-walled products during welding.

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