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In this paper we benchmark the performance of three algorithms for generating quad dominated surface meshes of the geometric models in ship structural analysis. We compare algorithms based on the combinatorial approach of packing the surfaces with parallelograms and those algorithms which are based on the variants of the Delaunay advancing front approaches. The meshing in ships structural analysis is specific in that the restrictions on the algorithm are defined by the rules of the ship classification societies which contain linear restrictions on the geometry. Linear restrictions are directly at odds with the principles of the Delaunay advancing front approaches. We present a specific quality indicator for assessing the quality of such meshes and compare three available algorithms in Gmsh. Finally, we assess the performance of our preconditioning strategy for these algorithms and argue for its suitability for the task.

We present a frontal, quad based, Delaunay meshing algorithm adapted to the structures appearing in the ship structural analysis. The main contribution of the paper is the preprocessing algorithm which resolves the geometry of the object and divides it into plates where all of the intersections of the boundary edges are guaranteed to be the nodes of any mesh generated for such a geometry. The result of this preprocessing algorithm is a discrete description of the geometry which can be meshed by the automatic frontal mesher according to the requirements of the classification society. Further algorithmic solutions for the inclusion of openings in the plates are also presented. The resulting algorithm is wholly implemented in python, using open source gmsh system together with the opencad module. It is capable of generating as many as ten thousand quads per second. This is the efficiency comparable to the standard triangular mesh algorithms and is due to the efficient implementation of the Delaunay quad algorithm in gmsh. We present several models from the engineering praxis to illustrate our claims.

U ovom radu opisali smo primjenu teorije linearizirane elastičnosti na 3D modele koronarnih stentova. Objasnili smo uz koje pretpostavke, i na koji način, smo izveli jednadžbe linearizirane elastičnosti te zašto je ta teorija primjenjiva na problem koji smo promatrali. Nadalje, modelirali smo nekoliko geometrija koronarnih stentova, detaljno opisali postupak nastajanja svakog 3D modela te samu prednost i jednostavnost pristupa problemu. Implementirali smo dvije formulacije za rješavanje problema linearizirane elastičnosti. Diskutirali smo o prednostima pojedinih geometrija, razlici dobivenih aproksimacija iz obje formulacije te dali smjernice za moguće daljnje istraživanje. In this work we describe an application of linearized elasticity on 3D models of coronary stents. We explaine how we derive equations of linearized elasticity and why are they applicable on our problem. We model several coronary stent geometries and thoroughly describe the whole procedure. Implementation of two formulations for solving linearized elasticity problem is given in this work. We discuss benefits of some geometries, difference of given approximations from both formulations and give guidelines for future research.