The Contact Problem at Delamination

1995 ◽  
Vol 62 (4) ◽  
pp. 989-996 ◽  
Author(s):  
A. E. Giannakopoulos ◽  
K.-F. Nilsson ◽  
G. Tsamasphyros
Keyword(s):  
Contact Problem ◽  
Plate Theory ◽  
Compressive Loading ◽  
Material Anisotropy ◽  
Intensity Factors ◽  
Finite Element Scheme ◽  
Contact Conditions ◽  
Delamination Buckling ◽  
Post Buckling ◽  
Delamination Front

The important phenomenon of delamination buckling is examined subjected to the condition of frictionless contact. Buckled delamination is examined in particular, because in-plane compressive loading is typical and detrimental. Two types of contact can be distinguished, local and global. The latter may occur everywhere in the plate while the local contact is limited to the crack front (negative KI stress intensity factors). Both local and global contact conditions were considered using a finite element scheme which employed nonlinear plate theory. The global contact problem is formulated as it appears in post-buckling of delamination. The case of simultaneous buckling and contact is also addressed in this paper. Two particularly interesting examples of thin film delaminations are presented. In the first, the contact at buckling is due to the material anisotropy. In this case the bucking load and the post-bucking analysis were very well supported by experiments. In the second example, contact at buckling arises because of a pin that holds down the delaminated layer at its center. The treated cases indicated that contact may significantly affect the fracture parameters along the delamination front, and is, therefore, important for delamination arrest.

Nonlinear thermo-mechanical buckling of higher-order shear deformable porous functionally graded material plates reinforced by orthogonal and/or oblique stiffeners

2019 ◽  
Vol 233 (17) ◽  
pp. 6177-6196 ◽  
Author(s):  
Vu Hoai Nam ◽  
Nguyen Thi Phuong ◽  
Dang Thuy Dong ◽  
Nguyen Thoi Trung ◽  
Nguyen Van Tue
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Functionally Graded Material ◽  
Thermal Environment ◽  
Plate Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Deformation Plate Theory ◽  
Graded Material ◽  
Post Buckling

In this paper, an analytical approach for nonlinear buckling and post-buckling behavior of stiffened porous functionally graded plate rested on Pasternak's elastic foundation under mechanical load in thermal environment is presented. The orthogonal and/or oblique stiffeners are attached to the surface of plate and are included in the calculation by improving the Lekhnitskii's smeared stiffener technique in the framework of higher-order shear deformation plate theory. The complex equilibrium and stability equations are established based on the Reddy's higher-order shear deformation plate theory and taken into account the geometrical nonlinearity of von Kármán. The solution forms of displacements satisfying the different boundary conditions are chosen, the stress function method and the Galerkin procedure are used to solve the problem. The good agreements of the present analytical solution are validated by making the comparisons of the present results with other results. In addition, the effects of porosity distribution, stiffener, volume fraction index, thermal environment, elastic foundation… on the critical buckling load and post-buckling response of porous functionally graded material plates are numerically investigated.

Viscoelastic Contact of a Half-Plane Sliding Over a Slightly Wavy Rigid Surface

2014 ◽  
Author(s):  
N. Menga ◽  
C. Putignano ◽  
T. Contursi ◽  
G. Carbone
Keyword(s):  
Contact Problem ◽  
Contact Area ◽  
Analytical Procedure ◽  
Sliding Contact ◽  
Rigid Surface ◽  
Viscoelastic System ◽  
Contact Conditions ◽  
Partial Contact ◽  
Full Contact ◽  
Viscoelastic Contact

In this paper, the sliding contact of a rigid sinusoid over a viscoelastic halfplane is studied by means of an analytical procedure that reduced the original viscoelastic system to an elastic equivalent one, which has been already solved in [1]. In such a way, the solution of the original viscoelastic contact problem requires just to numerically solve a set of two integral equations. Results show the viscoelasticity influence on the solution by means of a detailed analysis of contact area, pressure and displacement distribution. A particular attention is paid to the transition from full contact to partial contact conditions.

New higher order plate theory in modeling delamination buckling of composite laminates

AIAA Journal ◽  
1994 ◽  
Vol 32 (8) ◽  
pp. 1709-1716 ◽  
Author(s):  
Aditi Chattopadhyay ◽  
Haozhong Gu
Keyword(s):  
Composite Laminates ◽  
Plate Theory ◽  
Higher Order ◽  
Delamination Buckling

Hypersonic Flutter Analysis of Functionally Graded Panels under Thermal and Aerodynamic Loads

2009 ◽  
Vol 631-632 ◽  
pp. 41-46
Author(s):  
Sun Bae Kim ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Virtual Work ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Aerodynamic Loads ◽  
Linear Rule ◽  
Structural Nonlinearity ◽  
Post Buckling

In this work, hypersonic aero-thermo post-buckling and thermal flutter behaviors of Functionally Graded (FG) panels under thermal and aerodynamic loads are investigated. The volume fractions of constitutive materials of the panels are gradually varied from ceramic to metal in the thickness direction based on a simple power law distribution. Thus, the material properties of the panel are also changed by a linear rule of mixture. Furthermore, the material properties are assumed to be temperature dependent because the panels are mainly used in the high temperature environments. Using the principle of virtual work, the equations of motion of the first-order shear deformation plate theory (FSDPT) are derived and the finite element method is applied to get the solution. In the formulation, the von Karman strain-displacement relationship is used for structural nonlinearity, and the partial second-order piston theory is adopted to consider the aerodynamic nonlinearity. Newton-Raphson iterative technique is used to solve the governing equations, and linear eigenvalue analysis is performed to obtain the hypersonic flutter boundaries.

Imperfection Sensitivity of Post-Buckling Behavior and Vibration Response in Pre- and Post-Buckled Regions of Nanoscale Plates Considering Surface Effects

2018 ◽  
Vol 10 (03) ◽  
pp. 1850027 ◽  
Author(s):  
Raheb Gholami ◽  
Reza Ansari
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Displacement Vector ◽  
Vibration Response ◽  
Hamilton’S Principle ◽  
Imperfection Sensitivity ◽  
Hamilton's Principle ◽  
External Work ◽  
Buckling Behavior ◽  
Post Buckling

This paper aims to investigate the imperfection sensitivity of the post-buckling behavior and the free vibration response under pre- and post-buckling of nanoplates with various edge supports in the thermal environment. Formulation is based on the higher-order shear deformation plate theory, von Kármán kinematic hypothesis including an initial geometrical imperfection and Gurtin–Murdoch surface stress elasticity theory. The discretized nonlinear coupled in-plane and out-of-plane equations of motion are simultaneously obtained using the variational differential quadrature (VDQ) method and Hamilton’s principle. To this end, the displacement vector and nonlinear strain–displacement relations corresponding to the bulk and surface layers are matricized. Also, the variations of potential strain energies, kinetic energies and external work are obtained in matrix form. Then, the VDQ method is employed to discretize the obtained energy functional on space domain. By Hamilton’s principle, the discretized quadratic form of nonlinear governing equations is derived. The resulting equations are solved employing the pseudo-arc-length technique for the post-buckling problem. Moreover, considering a time-dependent small disturbance around the buckled configuration, the vibrational characteristics of pre- and post-buckled nanoplates are determined. The influences of initial imperfection, thickness, surface residual stress and temperature rise are examined in the numerical results.

Study on the Difference of the Propagation Characteristics between Open Flaws and close Flaws in Brittle Materials under Compressive Loading

2011 ◽  
Vol 197-198 ◽  
pp. 1406-1411 ◽  
Author(s):  
Qiang Li ◽  
Yan Liang Shang ◽  
Yang Wang ◽  
Ying Chun Fu
Keyword(s):  
Stress Intensity ◽  
Crack Propagation ◽  
Numerical Method ◽  
Stress Intensity Factors ◽  
Compressive Loading ◽  
Brittle Materials ◽  
Propagation Characteristics ◽  
Intensity Factors ◽  
Propagation Paths ◽  
Branch Crack

The second development of ABAQUS is implemented to simulate the initiation, propagation processes of flaws in brittle materials under compressive loading (in the paper ‘flaw’ means ‘the initial crack’, and ‘crack’ means ‘the branch crack’), by which the propagation paths and the corresponding stress intensity factors of the branch crack can be calculated. Further more the experiment is carried out to verify the validity of the above numerical method. By the numerical method, the propagation processes of open flaws and close flaws are simulated, and the comparative analysis of propagation characteristics between the open flaw and the close flaw is carried out. The results show the obvious difference in the propagation characteristics between open flaws and close flaws with the same initial flaw length and angle. Firstly, compared with the close flaw, the branch crack of the open flaw grows along a more obviously curvilinear path, and the propagation path gradually approaches to a line, which passes through the middle point of the open flaw and parallel to the maximum principal stress. Secondly in the early stage of the crack propagation, the stress intensity factors of the branch crack of the open flaw are greater than of the close flaw, but with the further propagation of the branch cracks, the stress intensity factors of the branch crack of the open flaw will be less than of the close flaw. Additionally, according to the close flaw, with the decrease of the friction coefficients, the curve characteristics of the crack propagation paths become more obvious. Therefore, it is noteworthy that the wing crack of the close flaw can be regard as the straight line if the friction coefficient of the flaw surface is very small. The above differences of the propagation characteristics between the open flaws and the close flaw show that the two flaws should be distinguished strictly in the fracture analysis.

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