Transformation of coordinate system

Given a transformation of coordinate system from to an orthogonal cnrvilinear coordinate... 

Tensor of pth order represents 3 quantities Tyki... that are transformed, under the transformation of coordinate system x = ayXj, according to the law... 

The reason that these approaches appear to be cumbersome is that and Cij, representations chosen for their convenience for calculation and ease of interpretation rather than their underlying mathematical structure, are not components of tensors. In particular, their components do not transform under transformation of coordinate systems as do the components of tensors. Consequently, before components of any physical quantity represented by a tensor of any order can be transformed from one coordinate system to another, the array must be put into its bona fide tensor form. 

The transformation of coordinate system is performed for each structural member. This allows one to enforce kinematic compatibility and equilibrium at all nodes connecting structural members. Then, the global dynamic system is constructed following classic direct stiffness procedure ... 

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