Non-prismatic Timoshenko-like beam model: Numerical solution via isogeometric collocation

Fast and accurate elastic analysis of laminated composite plates via isogeometric collocation and an equilibrium-based stress recovery approach

“…Therefore, we conclude that using a degree of approximation equal to 6 in-plane and equal to 4 through the thickness seems to be a reasonable choice to correctly reproduce the 3D stress state. Using instead uniform approximation degrees p = q = r = 6 does not seem to significantly improve the results (see Figures 8,9,and Table 2). The post-processing method provides better results for increasing values of length-to-thickness ratio and number of layers and therefore proves to be particularly convenient for very large and thin plates.…”

“…Isogeometric collocation has been particularly successful in the context of structural elements, where isogeometric collocation has proven to be particularly stable in the context of mixed methods. In particular, Bernoulli-Euler beam and Kirchhoff plate elements have been proposed [64], while mixed formulations both for Timoshenko initially-straight planar [17] and non-prismatic [9] beams as well as for curved spatial rods [8] have been introduced and studied, and then effectively extended to the geometrically nonlinear case [47,53,54,55,75,77]. Isogeometric collocation has been moreover successfully applied to the solution of Reissner-Mindlin plate problems in [44], and new formulations for shear-deformable beams [45,47], as well as shells [46,56] have been solved also via IGA collocation.…”

On the application of isogeometric finite volume method in numerical analysis of wet-steam flow through turbine cascades

“…More precisely, in the isogeometric framework, the computational mesh is inherently created by non-uniform rational B-spline (NURBS) description of the geometry and the governing equations are then discretized by transforming from the "curved" grids (of arbitrary degree) on the computational domain to the "rectangular" ones on the parameter space of the Bspline/NURBS geometry. Thanks to the accurate and efficient geometry representation of the IGA approach, it has been successfully implemented in various practical applications such as computational mathematics [2][3][4][5], electromagnetics [6,7], solid and fluid mechanics [8][9][10][11][12], fluid-structure interaction [13,14], heat transfer [15,16] and eigenvalue problems [17,18].…”

Studies on knot placement techniques for the geometry construction and the accurate simulation of isogeometric spatial curved beams

“…Isogeometric static and vibration analyses of curved beam structures have been taken into consideration by many researchers in recent years. We can categorize these research works into the two main groups of planar (see, e.g., [15][16][17][18][19][20][21]) and spatial (see, e.g., [22][23][24][25][26][27]) curved beam representations where the latter is more applicable in real-world engineering problems but needs a more complex formulation. Reviewing some recent works in this area, Bauer et al [23] have proposed a continuum element formulation for static analysis of geometrically nonlinear space curved beams assuming Euler-Bernoulli theory.…”