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Strong-form governing equations and solutions for variable kinematic beam theories with practical applications

Pagani, Alfonso (2016). Strong-form governing equations and solutions for variable kinematic beam theories with practical applications. (Unpublished Doctoral thesis, City, University of London)


Due to the work of pioneering scientists of the past centuries, the three-dimensional theory of elasticity is now a well-established, mature science. Nevertheless, analytical solutions for three-dimensional elastic bodies are generally available only for a few particular cases which represent rather coarse simplifications of reality. Against this background, the recent development of advanced techniques and progresses in theories of structures and symbolic computation have made it possible to obtain exact and quasi-exact resolution of the strongform governing equations of beam, plate and shell structures.

In this thesis, attention is primarily focused on strong-form solutions of refined beam theories. In particular, higher-order beam models are developed within the framework of the Carrera Unified Formulation (CUF), according to which the three-dimensional displacement field can be expressed as an arbitrary expansion of the generalized displacements.

The governing differential equations for static, free vibration and linearized buckling analysis of beams and beam-columns made of both isotropic and anisotropic materials are obtained by applying the principle of virtual work. Subsequently, by imposing appropriate boundary conditions, closed-form analytical solutions are provided wherever possible in the case of structures with uncoupled axial and in-plane displacements. The solutions are also provided for a wider range of structures by employing collocation schemes that make use of radial basis functions. Such method may be seriously affected by numerical errors, thus, a robust and efficient method is also proposed in this thesis by formulating a frequency dependant dynamic stiffness matrix and using the Wittrick-Williams algorithm as solution technique.

The theories developed in this thesis are validated by using some selected results from the literature. The analyses suggest that CUF furnishes a reliable method to implement refined theories capable of providing almost three-dimensional elasticity solution and that the dynamic stiffness method is extremely powerful and versatile when applied in conjunction with CUF.

Publication Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology
Doctoral Theses
School of Science & Technology > School of Science & Technology Doctoral Theses
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