Vibration of cracked structures: A state of the art review

Modeling metal deposition in heat transfer analyses of additive manufacturing processes

Adaptive finite element methods (FEM) have been widely used in applications for over 20 years now. In practice, they converge starting from coarse grids, although no mathematical theory has been able to prove this assertion. Ensuring an error reduction rate based on a posteriori error estimators, together with a reduction rate of data oscillation (information missed by the underlying averaging process), we construct a simple and efficient adaptive FEM for elliptic partial differential equations. We prove that this algorithm converges with linear rate without any preliminary mesh adaptation nor explicit knowledge of constants. Any prescribed error tolerance is thus achieved in a finite number of steps. A number of numerical experiments in two and three dimensions yield quasi-optimal meshes along with a competitive performance. Extensions to higher order elements and applications to saddle point problems are discussed as well.

Keywords: A posteriori error estimators, data oscillation, adaptive mesh refinement, convergence, Stokes, Uzawa

AMS Subject Classifications: 65N12, 65N15, 65N30, 65N50, 65Y20


Published: SIAM Review, 44 (2002) 631--658.

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Convergence of Adaptive Finite Element Methods

Simulation of welding has advanced from the analysis of laboratory setups to real engineering applications during the last three decades. This development is outlined and the directions for future research are summarized in this review, which consists of three parts. This part shows that the increased complexity of the models gives a better description of the engineering applications. The important development of material modeling and computational efficiency are outlined in Parts 2 and 3, respectively.

Finite element modeling and simulation of welding part 1: increased complexity

Simulation of welding has advanced from the analysis of laboratory setups to real engineering applications during the last three decades. This development is outlined and the directions for future research are summarized in this review, which consists of three parts. The material modeling is maybe the most crucial and difficult aspect of modeling welding processes. The material behavior may be very complex for the large temperature range considered.

Finite element modeling and simulation of welding. part 2: improved material modeling

The problem of determining temperature distributions, transient thermal strains, and residual stresses during butt welding thick plates with the multipass GMAW process is solved using the finite element method. First, a nonlinear heat transfer analysis is performed taking into account the temperature dependence of the material properties, and convection and radiation surface heat losses. This is followed by a thermo-elastic-plastic stress analysis that incorporates phase transformation strains. Finally, the theoretical predictions are compared with experimentally obtained data showing good correlation.

Numerical analysis of thermal stresses during welding including phase transformation effects

Hydrogen effect on fracture toughness of pipeline steel welds, with in situ hydrogen charging

Deep water mooring dynamics

Hydrogen effect on a low carbon ferritic-bainitic pipeline steel

Using a new FE modelling procedure for the accurate representation of a geometrically imperfect cylinder, the present study investigates the effect of the initial imperfection magnitude on the cylinder buckling load, when it is loaded by external hydrostatic pressure. The buckling behaviour of a carbon/epoxy filament wound cylinder is initially studied and the modelling procedure is validated through a comparison between calculated and experimental results. Various FE models are developed and evaluated, with increasing degree of complexity. The method is then applied to a cylinder with different end supports, to assess how the boundary conditions together with the imperfections affect the buckling behaviour. Finally, the effect of imperfection magnitude is investigated, leading to the calculation of knockdown factors as low as 0.6.

V.J. Papazoglou

Papers

Numerical analysis of thermal stresses during welding including phase transformation effects

Hydrogen effect on fracture toughness of pipeline steel welds, with in situ hydrogen charging

Deep water mooring dynamics

Hydrogen effect on a low carbon ferritic-bainitic pipeline steel

The effect of geometric imperfections on the buckling behaviour of composite laminated cylinders under external hydrostatic pressure