The present paper describes the arc-length continuation method; a mathematical technique that can solve a wide variety of chemical engineering problems. Several case studies involving distillation, reaction engineering, and thermodynamics are treated with the help of this method. The approach is powerful enough to elucidate situations when several turning points occur. Finally, the authors conc...

We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the “coarse model” (the continuum, effective equation) need not be explicitly constructed. The method only uses a time-integration code for the discrete problem and judicious choices of initial data and integration times; our bifur...

The dynamics of beams that undergo large displacements is analyzed in frequency domain and comparisons between models derived by isogeometric analysis and p-FEM are presented. The equation of motion is derived by the principle of virtual work, assuming Timoshenko’s theory for bending and geometrical type of nonlinearity. As a result, a nonlinear system of second order ordinary differential equa...

PURPOSE An initial description of a sonographic finding predictive of intrathoracic chest tube placement. METHODS This was a prospective observational study using unembalmed cadaveric models. Chest tubes were randomly placed intra- and extrathoracically and evaluated using ultrasound. Chest tube location was confirmed using blunt dissection followed by tactile and visual confirmation. Sonogra...

The arc-length method is a powerful solution technique becoming increasingly popular among researchers and engineers. This method is presented here as a particular case of a more general formulation which includes all other solution strategies. The arc-length method is derived in its continuous and discrete formulations. Two versions of the arc-length method (Crisfield and Ramm) are presented a...

Geometrically nonlinear forced vibrations of three dimensional structures, due to harmonic excitations, are investigated in the frequency domain. Structures of elastic materials are considered and the discretized equation of motion is derived by the finite element method, using Elmer software. The shooting and the continuation methods are applied to the resulting large scale FEM system by using...

The nonlinear steady state large amplitude forced vibration response of a laminated composite annular sector plate is presented. governing equation motion the has been obtained using kinematics first-order shear deformation theory (FSDT) and employing Hamilton’s principle. equations have solved in time domain modified shooting method arc-length/pseudo-arc length continuation technique. influenc...

Arch-shaped microelectromechanical systems (MEMS) have been used as mechanical memories, micro-relays, micro-valves, optical switches and digital micro-mirrors. A bi-stable structure, such as an arch, is characterized by a multivalued load deflection curve. Here we study the symmetry breaking, the snap-through instability and the pull-in instability of a bi-stable arch-shaped MEMS under static ...

The eeect of using grid adaptation on the numerical solution of model convection-diiusion equations with a conservation form is studied. The grid adaptation technique studied is based on moving a xed number of mesh points to equidistribute a generalisation of the arc-length of the solution. In particular a parameter dependent monitor function is introduced which incorporates xed meshes, approxi...