3.0

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When the mechanical behavior of a structure is analyzed numerically, in many cases, the shell finite element method is the best choice. Examples include (see below) classic curved shell structures (roof domes, silos, storage tanks, cooling towers, etc.), bodies of ships, submarines, aircraft, missiles, also structural components (corrugated sheathing, plated beam/column members, etc.), but also biological “structures” (blood vessels, the human ear, etc.). In general, a shell finite element model is the natural mechanical numerical model for any object which can be interpreted geometrically as an assembly of surfaces. In most of the situations, especially if the surfaces are “not too curved”, flat shell finite elements can be used, while if the surfaces are "significantly curved”, curved shell elements can be beneficial. The literature of shell finite elements is immense; hence, the course focuses mostly on the basics, providing an introduction to how shell finite elements are developed, can be utilized, and what the potential difficulties and challenges are. Specific topics are as follows: · Introduction to and overview of the finite element method. · Flat membranes, membrane stress/strain finite elements. · Kirchhoff thin-plate theory, linear analysis, buckling analysis, modal vibration analysis: analytical solutions, FE implementations. · The effect of through-thickness shear, shear deformation plate theories (e.g., Mindlin): analytical solutions, FE implementations. · Issues: discontinuity, shear locking, zero-energy modes, drilling DOF. · Illustrations of the effect of curved geometry: analytical solutions, FE implementations. During the course we will develop simple FE codes in MATLAB.