2D finite elements for the computational analysis of crack propagation in brittle materials and the handling of double discontinuities

Crack growth simulations by way of the traditional Finite Element Method claim progressive remeshing to fit the geometry of the fracture, severely increasing the computational effort. Methods such as the eXtended Finite Element Method (XFEM) allow to overcome this limitation by means of nodal shape functions multiplied by Heaviside step function to enrich finite element nodes. Through the medium of a discontinuous field, the entire geometry of the discontinuity can be modelled regardless of the mesh, avoiding remeshing. In this paper two shell-type XFEM elements (a three-node triangular element and a four-node quadrangular element) to evaluate crack propagation in brittle materials are presented. These elements have been implemented into the widespread opensource framework OpenSees to evaluate crack propagation into a plane shell subjected to monotonically increasing loads. Moreover, in the perspective of fracture propagation simulations, the problem of managing multiple cracks without remeshing or operating subdivisions on the integration domain has been investigated and a four-node quadrangular finite element for the computational analysis of double crossed discontinuities by the means of equivalent polynomials is presented in this paper. Equivalent polynomials allow to overcome inaccuracies on the results when performing standard numerical integration (e.g. Gauss-Legendre quadrature rule) over the entire domain of XFEM elements, without the need of defining integration subdomains. The presented work and the computational strategy behind it may be extremely useful not only in the field of fracture mechanics, but also to solve complex geometry problems or material discontinuities

EQP - A 2D/3D library for integration of polynomials times step function

The EQuivalent Polynomials library, EQP, herein provided is a powerful tool for the numerical integration, with classical quadrature rules (e.g. Gauss–Legendre), of a function given by the product of an arbitrary polynomial times a Heaviside step function. The library can handle a multiplicity of shapes for the integration domain in one, two and three dimensions. Originally developed by Ventura Ventura,2006) to overcome the long-standing problem of integrating discontinuous functions in the context of the eXtended Finite Element Method, EQP library has been recently generalized to meet the needs of very different fields, spanning from computational mechanics, to computer graphics, evaluation of geometric region (mass) properties and computer simulation in general

Integration of Polynomials Times Double Step Function in Quadrilateral Domains for XFEM Analysis

The numerical integration of discontinuous functions is an abiding problem addressed by various authors. This subject gained even more attention in the context of the extended finite element method (XFEM), in which the exact integration of discontinuous functions is crucial to obtaining reliable results. In this scope, equivalent polynomials represent an effective method to circumvent the problem while exploiting the standard Gauss quadrature rule to exactly integrate polynomials times step function. Certain scenarios, however, might require the integration of polynomials times two step functions (i.e., problems in which branching cracks, kinking cracks or crack junctions within a single finite element occur). In this context, the use of equivalent polynomials has been investigated by the authors, and an algorithm to exactly integrate arbitrary polynomials times two Heaviside step functions in quadrilateral domains has been developed and is presented in this paper. Moreover, the algorithm has also been implemented into a software library (DD_EQP) to prove its precision and effectiveness and also the proposed method’s ease of implementation into any existing computational software or framework. The presented algorithm is the first step towards the numerical integration of an arbitrary number of discontinuities in quadrilateral domains. Both the algorithm and the library have a wide application range, in addition to fracture mechanics, from mathematical computing of complex geometric regions, to computer graphics and computational mechanics

Bifurcations of Natural Convection Flows from an Enclosed Cylindrical Heat Source

A numerical analysis of transitional natural convection from a confined thermal source is presented. The system considered is an air-filled, square-sectioned 2D enclosure containing a horizontal heated cylinder. The resulting flow is investigated with respect to the variation of the Rayleigh number, for three values of the aspect ratio A. The first bifurcation of the low-Ra fixed-point solution is tracked for each A-value. Chaotic flow features are detailed for the case A = 2.5. The supercritical behaviour of the system is investigated using nonlinear analysis tools and phase-space representations, and the effect of the flow on heat transfer is discussed

High-Bandwidth Morphing Actuator for Aeroelastic Model Control

© 2019 by the authors. The design and testing of a high-bandwidth continuous actuator for aeronautical applications is presented hereinafter. The actuator has a dual goal of controlling both the aeroelastic behaviour and the flight mechanics of the model in which it is installed. In order to achieve these aims, the actuation bandwidth of the active aerofoil, as well as its static camber variation, have to be sufficiently high. The camber morph is achieved by using tailored piezoelectric patches in a sandwich configuration with a linear trailing edge slider to allow the necessary compliance. The morphing actuator is designed for a NACA 0018 aerofoil with a chord of 300mmand a span of 40 mm. Static and dynamic experimental tests are carried out on a prototype, and a camber variation control technique is implemented. It is proved that the actuator bandwidth is up to 25 Hz and the equivalent maximum deflection is ±15 degrees. This solution is shown to be a viable light-weight alternative to the conventional brushless/servo-motor approach currently used in aeroelastic models

Experimental Nonlinear Control for Flutter Suppression in a Nonlinear Aeroelastic System

Experimental implementation of input–output feedback linearization in controlling the dynamics of a nonlinear pitch–plunge aeroelastic system is presented. The control objective is to linearize the system dynamics and assign the poles of the pitch mode of the resulting linear system. The implementation 1) addresses experimentally the general case where feedback linearization-based control is applied using as the output a degree of freedom other than that where the physical nonlinearity is located, using a single trailing-edge control surface, to stabilize the entire system; 2) includes the unsteady effects of the airfoil’s aerodynamic behavior; 3) includes the embedding of a tuned numerical model of the aeroelastic system into the control scheme in real time; and 4) uses pole placement as the linear control objective, providing the user with flexibility in determining the nature of the controlled response. When implemented experimentally, the controller is capable of not only delaying the onset of limit-cycle oscillation but also successfully eliminating a previously established limit-cycle oscillation. The assignment of higher levels of damping results in notable reductions in limit-cycle oscillation decay times in the closed-loop response, indicating good controllability of the aeroelastic system and effectiveness of the pole-placement objective. The closed-loop response is further improved by incorporating adaptation so that assumed system parameters are updated with time. The use of an optimum adaptation parameter results in reduced response decay times