A great deal of understanding into the behaviour of composite steel-concrete structures in fire has been developed since the Cardington frame fire tests (UK) 1990s. This has now been broadened so that structures in fire design has a real engineering basis and is not reliant on results from single element testing in the standard furnace. Several projects involving office buildings in the UK and ...

Shape gradients of PDE constrained shape functionals can be stated in two equivalent ways. Both rely on the solutions of two boundary value problems (BVPs), but one involves integrating their traces on the boundary of the domain, while the other evaluates integrals in the volume. Usually, the two BVPs can only be solved approximately, for instance, by finite element methods. However, when used ...

A computational method is presented for optimizing needle placement in radiofrequency ablation treatment planning. The parameterized search is guided by an objective function that depends on transient, finite element solutions of coupled thermal and potential equations for each needle placement. A framework is introduced for solving the electrostatic equation by using boundary elements to model...

We deduce discrete compactness of Rellich type for some discontinuous Galerkin finite element methods (DGFEM) including hybrid ones, under fairly general settings on the triangulations and the finite element spaces. We make use of regularity of the solutions to an auxiliary second-order elliptic boundary value problem as well as the error estimates of the associated finite element solutions. Th...

In this article, the multi-objective optimization of cylindrical aluminum tubes under axial impact load is presented.The absorbed energy and the specific absorbed energy (SEA) are considered as objective functions while the maximum crush load should not exceed allowable limit. The geometric dimensions of tubes including diameter, length and thickness are chosen as design variables. The Non-domi...

In the present study, free vibration behaviors of of carbon nanotube (CNT) and boron nitride nanotube (BNNT) have been investigated via Eringen’s nonlocal continuum theory. Size effect has been considered via nonlocal continuum theory. Nanotubes have become popular in the world of science thanks to their characteristic properties. In this study, free vibrations of Boron Nitride Nanotube (BNNT) ...

The coordinate transformation for quadrilateral isoparametric elements is well-defined in the finite element literature. However, a corresponding inverse transformation is not found. In fact, it has been commonly believed that no explicit solutions to the inverse transformation problem exist. This paper shows that if geometric considerations are used, a complete set of general solutions to the ...

We consider the imposition of Dirichlet boundary conditions in the finite element modelling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The validity of the technique is assessed f...

where Ω ⊂ R, ∂ΩD ∪ ∂ΩN = ∂Ω and the two boundary regions are distinct with ∂ΩD non-empty. Specifically, we will consider the key results in the development of the theory of finite elements, including weak solutions and the structure of the individual elements, as well as the numerical implementation of the method. We will subsequently implement a finite element numerical solver in order to solv...

The DtN finite element method for solving the exterior Helmholtz problem is mathematically analyzed. The reduced problem with DtN artificial boundary condition is shown to be equivalent to the original exterior problem. Error estimates for solutions obtained by the DtN finite element method are established.