While all engineering structures are 3D -- satisfactory approximations
may often be obtained by using simplifications to 1D or 2D based on the
geometry
and loading.
Classification of structures
1D
One dimension is significantly larger than other 2 dimensions.
1.Truss : Loading and geometry are both along
the same line.
2.Beam : Geometry is 1D but loading is 3D. Assumptions
are used on the behaviour through the depth and thickness. For long
slender beams (L >
10h,10d) "plane sections remain
plane and normal to the neutral axis" => linear variation of displacement
in directions normal to the length.
2D
Plane solids: The third dimension is either very small/very large relative to the first two, the geometry is flat AND the loads are in the same plane.
1. Plane
strain: Third direction strains are very small and are neglected.
2. Plane
stress: Third direction stresses are very small and neglected.
Plate The third dimension is very small, the geometry is planar(flat) AND the loads are out of the plane.
Shell The third dimension is either very small/very large relative to the first AND the loads are out of the plane AND the geometry is curvilinear.
Axisymmetric The solid can be generated by revolving a 2D section
about an axis.