G. Tsamasphyros

Dynamic Response of Circular GLARE Fiber-Metal Laminates Subjected to low Velocity Impact

This article deals with the dynamic response of thin circular clamped GLARE fiber—metal laminates subjected to low velocity impact by a lateral hemispherical impactor. Using a spring-mass model, the differential equations of motion corresponding to loading and unloading stages of impact are derived and solved numerically. Internal damage due to delamination is taken into account. Previously published analytical formulas1,2 concerning the indentation of circular GLARE plates are used during the loading stages of impact. In this study, an equation for the unloading path is derived and used during the unloading impact stage. The load—time, position—time, velocity—time, and kinetic energy—time history responses are calculated. In this regard, the position where delamination occurs, the maximum plate deformation and the position where the impact load becomes zero are predicted. Also, the maximum impact load and the total impact duration are determined. The derived differential equations of motion are applied for GLARE 4-3/2 and GLARE 5-2/1 circular plates subjected to low velocity impact. The predicted load—time history response is compared with published experimental data and a good agreement is found. No other solution of this problem is known to the authors.

Automatic optimum mesh around singularities using conformal mapping

Abstract Geometrical discontinuities create singular fields. For the confrontation of such singularities, a gradual concentration of the finite element mesh is needed around the point of geometrical discontinuity. The automatic generation of an optimal mesh is obtained by using a Schwarz-Christoffel conformal transformation. Some characteristic examples are given in order to illustrate the method. The quality of the meshes produced is checked in a number of examples, and very satisfactory results are obtained.

Application of bi-Helmholtz nonlocal elasticity and molecular simulations to the dynamical response of carbon nanotubes

The nonlocal theory of elasticity is employed for the study of the free vibrations of carbon nanotubes (CNT). For the first time, a bi-Helmholtz operator has been used instead of the standard Helmholtz operator in a nonlocal beam model. Alongside the continuum formulation and its numerical solution, atomistic Molecular Dynamics (MD) simulations have been conducted in order to directly evaluate the eigenfrequencies of vibrating CNTs with a minimum of adjustable parameters. Our results show that the bi-Helmholtz operator is the most appropriate one to fit MD simulation results. However, the estimation of vibration eigenfrequencies from molecular simulations still remains an open (albeit well-posed) problem.

An alternating coupling of finite elements and singular integral equations for the solution of branched cracks in finite sheets

Abstract The problem of a branched crack in a finite sheet is considered in this paper. The solution is given by Schwarzs alternating method, using two sequences of solutions. The first sequence corresponds to the finite, but uncracked, body, and the finite element method was used, whereas for the other sequence of solutions concerning the infinite cracked sheet, the singular integral equation method. In this way, the well-known capabilities of singular integral equations to describe accurately singular fields with the flexibility and the stability of finite element method are efficiently combined to solve rapidly, and with a reduced computer cost, complicated problems of cracked plates encountered in the praxis. Numerical applications of the method proved the rapid convergence and the stability of the procedure, as well as its accuracy and versatility.

Quasi-Static Response of Circular Glare Plates Subjected to Low Velocity Impact

The response of circular GLARE fiber-metal laminates subjected to low velocity impact by a hemispherical impactor is treated analytically. Using a quasi-static approach, characteristic impact variables are calculated. A force-deflection relation is determined and employed for the unloading impact stage. Delamination is also considered. Application to GLARE 4-3/2 and GLARE 5-2/1 plates is implemented. The predicted maximum impact load, its application time, and the total impact duration agree well with published experiments. The derived formulas can be used to evaluate impact response of GLARE or other similar hybrid laminates. No other solution of this problem is known to the authors.

A Gauss quadrature formula for Cauchy type integrals

AbstractIn this paper, a set of polynomials {ϕn(x;ζ)} orthogonal with respect to w(x)/(x − ζ) is obtained. (w(x) being a weight function.) Using these polynomials a Gauss formula for the numerical integration of the Cauchy type integrals

An integral-equation solution for cracked half-planes bonded together and containing debondings along their interface

I(f;\xi ) = \mathop {\rlap{--} \smallint }\limits_a^b \frac{{w(x)f(x)}}{{x - \xi }}{\text{d}}x

Stress intensities in a strip reinforced by stiffeners at the edges

is for the first time constructed. The proof follows the same lines as the proof of the classical Gauss integration for the Riemann integrals. The proposed quadrature formula is very interesting in many problems of mathematical physics, mechanics etc.The new formula presents the expected polynomial accuracy and it is succesfully tested in three numerical examples.