Under the curvilinear coordinate system
, a curved girder finite element with 3 nodes which has 7 degrees of freedom per node has been constructed and the corresponding shape functions have been constructed.
9] developed 3D set of field equations of FGM thick shells of revolution in curvilinear coordinate system by tensor calculus.
Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system, Mechanika 77(3): 18-26.
A new curvilinear coordinate system
tool makes it easier to define anisotropic materials in curved geometric shapes.
1]([phi]), one can readily define a non-orthogonal curvilinear coordinate system u - [phi] as
It is also possible to define an orthogonal curvilinear coordinate system u - v as the following
A simple geometric observation model and computations can be used in such a space, but application of such polar observations in a space of the global geographical coordinate system is complicated, because we come into collision with the curvilinear coordinate system
related to the surface of an ellipsoid.
dagger]) For instance, in flat spacetime one can introduce a curvilinear coordinate system
of coordinates, like the use of polar coordinates in the plane and spherical coordinates in [R.
Using tensor analysis, which is extremely useful especially for three-dimensional problems in any curvilinear coordinate system
, a number of researchers, including Fung , Green and Zerna  have developed the general theory of elasticity.
Coverage progresses from the algebra of vectors and vector functions of one variable, through integral theorems and orthogonal curvilinear coordinate systems