This paper presents the formulation of advanced one-dimensional finite elements for the geometrically non-linear static analysis of beams. The kinematic field is axiomatically assumed along the thickness direction via a Unified Formulation. The approximation order of the displacement field along the thickness is a free parameter that leads to the formulation of a family of several beam elements. The tangent stiffness matrix of the element is obtained via the Principle of Virtual Displacements. A total Lagrangian approach is used. Newton-Raphson method is employed in order to solve the non-linear governing equations. Numerical investigations in terms of displacements and stresses are validated towards two-dimensional FEM solutions in order to show the correctness and the advantages of the proposed modelling approach.

Geometrically nonlinear hierarchical finite elements via a unified formulation / DE PIETRO, Gabriele; G., Giunta; S., Belouettar; Pagani, Alfonso; Carrera, Erasmo. - (2017). (Intervento presentato al convegno 20th International Conference on Composite Structures (ICCS20) tenutosi a Paris, France nel 4-7 September 2017).

Geometrically nonlinear hierarchical finite elements via a unified formulation

DE PIETRO, GABRIELE;PAGANI, ALFONSO;CARRERA, Erasmo
2017

Abstract

This paper presents the formulation of advanced one-dimensional finite elements for the geometrically non-linear static analysis of beams. The kinematic field is axiomatically assumed along the thickness direction via a Unified Formulation. The approximation order of the displacement field along the thickness is a free parameter that leads to the formulation of a family of several beam elements. The tangent stiffness matrix of the element is obtained via the Principle of Virtual Displacements. A total Lagrangian approach is used. Newton-Raphson method is employed in order to solve the non-linear governing equations. Numerical investigations in terms of displacements and stresses are validated towards two-dimensional FEM solutions in order to show the correctness and the advantages of the proposed modelling approach.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2686810
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