Long arithmetic in Excel. III. Solution of systems of linear algebraic equations for test problems of the finite element modelling

2019 ◽  
Vol 12 ◽  
Author(s):  
V. Fourman ◽  
M. Khomyak ◽  
Ya. Marko
Keyword(s):  
Finite Element ◽  
Finite Element Modelling ◽  
Test Problems ◽  
Algebraic Equations ◽  
Element Modelling ◽  
Linear Algebraic Equations

TWO-DIMENSIONAL LARGE DEFORMATION FINITE ELEMENT MODELLING OF SENSITIVE CLAY LANDSLIDES

2020 ◽  
Author(s):  
Bipul Hawlader ◽  
◽  
Chen Wang ◽  
Ripon Karmaker ◽  
Didier Perret ◽  
...  
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Finite Element Modelling ◽  
Two Dimensional ◽  
Element Modelling ◽  
Sensitive Clay

scholarly journals Size Effects in Finite Element Modelling of 3D Printed Bone Scaffolds Using Hydroxyapatite PEOT/PBT Composites

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1746
Author(s):  
Iñigo Calderon-Uriszar-Aldaca ◽  
Sergio Perez ◽  
Ravi Sinha ◽  
Maria Camara-Torres ◽  
Sara Villanueva ◽  
...  
Keyword(s):  
Finite Element ◽  
Additive Manufacturing ◽  
Tissue Regeneration ◽  
Finite Element Modelling ◽  
Bulk Material ◽  
Bone Tissue Regeneration ◽  
Patient Specific ◽  
Design Factor ◽  
Element Modelling ◽  
Uncertainty Sources

Additive manufacturing (AM) of scaffolds enables the fabrication of customized patient-specific implants for tissue regeneration. Scaffold customization does not involve only the macroscale shape of the final implant, but also their microscopic pore geometry and material properties, which are dependent on optimizable topology. A good match between the experimental data of AM scaffolds and the models is obtained when there is just a few millimetres at least in one direction. Here, we describe a methodology to perform finite element modelling on AM scaffolds for bone tissue regeneration with clinically relevant dimensions (i.e., volume > 1 cm3). The simulation used an equivalent cubic eight node finite elements mesh, and the materials properties were derived both empirically and numerically, from bulk material direct testing and simulated tests on scaffolds. The experimental validation was performed using poly(ethylene oxide terephthalate)-poly(butylene terephthalate) (PEOT/PBT) copolymers and 45 wt% nano hydroxyapatite fillers composites. By applying this methodology on three separate scaffold architectures with volumes larger than 1 cm3, the simulations overestimated the scaffold performance, resulting in 150–290% stiffer than average values obtained in the validation tests. The results mismatch highlighted the relevance of the lack of printing accuracy that is characteristic of the additive manufacturing process. Accordingly, a sensitivity analysis was performed on nine detected uncertainty sources, studying their influence. After the definition of acceptable execution tolerances and reliability levels, a design factor was defined to calibrate the methodology under expectable and conservative scenarios.

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