Abstract
The hierarchical Timoshenko beam finite element, described in an earlier paper, is transformed into modal co-ordinates. The degrees of freedom of the new element are the deflection and cross section rotation at the two nodes together with an arbitrary number of coefficients of the elements clamped-clamped modes. Hence only two degrees of freedom are made continuous at an element boundary, permitting incorporation into user-oriented programs. Whereas displacement and shear deformation have to be considered separately in the previous formulation, these are combined by the use of modal variables, reducing the element degrees of freedom to the nodal variables and a single hierarchy of an arbitrary number of modal coefficients. Examples illustrating the use and accuracy of the element are given.
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