Shell Structures

This course covers analytical and numerical methods for analysing shell structures. The following is an overview of the key terms that will be further explored within this course:

Sagitta, a/t Ratio, Corbel dome, Arches, Catenary, Pressure lines, Middle third rule, Optimal arch shape, Barlow's formula, Thin or thick shells, Section forces and moments, Force flow in a dome, Edge disturbance, Comparison of moments in arches and domes, Optimal dome shape, Curvature, Gaussian curvature and mean curvature, Orthogonal parameterisation, Curvilinear coordinate system, Lame parameters, Equations of Gauss and Codazzi, In plane curvature, Shell membrane equations, Membrane forces in a spherical dome, Derivation of the membrane equations, Stresses in a simply supported tube, Comparison to a beam model, Bernoulli's hypothesis, Deformation of a simply supported tube, Misfit at the boundaries, Tube edge disturbance, Sanders-Koiter equations, Compatibility equation, Shell differential equations, Plate boundary conditions, Edge shear stresses, In plane shear forces, Derivation of Sander-Koiter equation 6, Shell boundary conditions, Dependent quantities, Generalised edge disturbance, Beam supported by springs, Influence length, Shell finite element types, Nodes and integration points, Mesh locking and hourglass modes, Benchmarks, Model size restrictions, Finite element analysis of a 4-hypar shell, Interpreting shell finite element results, Hypar curvature, Reinforcement, Particle-spring method, Timber grid shells, In-extensional deformation, Theorema egregium, Gauß-Bonnet theorem, Formulas for point loads, Trajectories, Umbilical patterns, Finite element analysis of a conoid, Natural frequencies, Linear buckling analysis, Non-linear analysis, Cylinder buckling shapes, Differential equation for shell buckling, Buckling load factor, Design check of buckling, Imperfection sensitivity, Exceptions to imperfection sensitivity, Koiter's law, Knock down factor, Linear buckling analysis, Nonlinear finite element analysis, Measuring shape imperfections, Stiffeners, Modal analysis, Rigid body modes, Equation of motion, Wave numbers, Vibration of hemispheres, spheres and cylinders, Natural frequency of a square shell, Measuring vibrations, Transient analysis, Damping ratio, Partial safety factors, Computation of failure probability, Acceptable failure probability, Many examples of remarkable shell structures.