An extended finite element model for modelling localised fracture of reinforced concrete beams in fire

Open Access funded by Engineering and Physical Sciences Research Council under a Creative Commons license.A robust finite element procedure for modelling the localised fracture of reinforced concrete beams at elevated temperatures is developed. In this model a reinforced concrete beam is represented as an assembly of 4-node quadrilateral plain concrete, 3-node main reinforcing steel bar, and 2-node bond-link elements. The concrete element is subdivided into layers for considering the temperature distribution over the cross-section of a beam. An extended finite element method (XFEM) has been incorporated into the concrete elements in order to capture the localised cracks within the concrete. The model has been validated against previous fire test results on the concrete beams.The Engineering and Physical Sciences Research Council of Great Britain under Grant No. EP/I031553/1

Aerodynamic preliminary analysis system 2. Part 1: Theory

An aerodynamic analysis system based on potential theory at subsonic and/or supersonic speeds and impact type finite element solutions at hypersonic conditions is described. Three dimensional configurations having multiple nonplanar surfaces of arbitrary planform and bodies of noncircular contour may be analyzed. Static, rotary, and control longitudinal and lateral directional characteristics may be generated. The analysis was implemented on a time sharing system in conjunction with an input tablet digitizer and an interactive graphics input/output display and editing terminal to maximize its responsiveness to the preliminary analysis problem. The program provides an efficient analysis for systematically performing various aerodynamic configuration tradeoff and evaluation studies

A Second Order Linear Discontinuous Cut-Cell Discretization for the SN Equations in RZ Geometry

In this dissertation we detail the development, implementation, and testing of a new cut-cell discretization for the discrete ordinates form of the neutron transport equation. This method provides an alternative to homogenization for problems containing material interfaces that do not coincide with mesh boundaries. A line is used to represent the boundary between the two materials in a mixed-cell converting a rectangular mixed-cell into two non-orthogonal, homogeneous cut-cells. The linear-discontinuous Galerkin finite element method (LDGFEM) spatial discretization is used on all of the rectangular cells as well as the non-orthogonal sub-cells. We have implemented our new cut-cell method in a test code which has been used to evaluate its performance relative to homogenization. We begin by developing the equations and methods associated with the LDGFEM discretization of the transport equation in RZ geometry for a homogenous orthogonal mesh. Next we introduce cut-cell meshes and develop a modification to the LDGFEM equations to account for material interfaces. We also develop methods to account for meshing errors encountered when representing curved material interfaces with linear cell faces. Finally we present test problems including manufactured solutions, fixed source, and eigenvalue problems for geometries with curvilinear material interfaces. The results of these test problems show the new cut-cell discretization to be second-order convergent for the scalar flux removed from singularities in the solution, as well as significantly more computationally efficient than homogenization

Arbitrary order 2D virtual elements for polygonal meshes: Part II, inelastic problem

The present paper is the second part of a twofold work, whose first part is reported in [3], concerning a newly developed Virtual Element Method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic problem. The aim of this part is to explore the features of the VEM formulation when material nonlinearity is considered, showing that the accuracy and easiness of implementation discovered in the analysis inherent to the first part of the work are still retained. Three different nonlinear constitutive laws are considered in the VEM formulation. In particular, the generalized viscoplastic model, the classical Mises plasticity with isotropic/kinematic hardening and a shape memory alloy (SMA) constitutive law are implemented. The versatility with respect to all the considered nonlinear material constitutive laws is demonstrated through several numerical examples, also remarking that the proposed 2D VEM formulation can be straightforwardly implemented as in a standard nonlinear structural finite element method (FEM) framework

On the use of quarter-point tetrahedral finite elements in linear elastic fracture mechanics

This paper discusses the reproduction of the square root singularity in quarter-point tetrahedral (QPT) finite elements. Numerical results confirm that the stress singularity is modeled accurately in a fully unstructured mesh by using QPTs. A displacement correlation (DC) scheme is proposed in combination with QPTs to compute stress intensity factors (SIF) from arbitrary meshes, yielding an average error of 2–3%. This straightforward method is computationally cheap and easy to implement. The results of an extensive parametric study also suggest the existence of an optimum mesh-dependent distance from the crack front at which the DC method computes the most accurate SIFs