Abstract
In this paper, a simplified approach to identify sectional deformation modes of prismatic cross-sections is presented and utilized in the establishment of a higher-order beam model for the dynamic analyses of thin-walled structures. The model considers the displacement field through a linear superposition of a set of basis functions whose amplitudes vary along the beam axis. These basis functions, which describe basis deformation modes, are approximated from nodal displacements on the discretized cross-section midline, with interpolation polynomials. Their amplitudes acting in the object vibration shapes are extracted through a modal analysis. A procedure similar to combining like terms is then implemented to superpose basis deformation modes, with equal or opposite amplitude, to produce primary deformation modes. The final set of the sectional deformation modes are assembled with primary deformation modes, excluding the ones constituting conventional modes. The derived sectional deformation modes, hierarchically organized and physically meaningful, are used to update the basis functions in the higher-order beam model. Numerical examples have also been presented and the comparison with ANSYS shell model showed its accuracy, efficiency, and applicability in reproducing three-dimensional behaviors of thin-walled structures.
Highlights
Thin-walled structures are commonly used in civil, aeronautical, and mechanical engineering structures
∂x ψ H ρHψ dAdz where V, A and L are the volume, the cross-section area and the length of the structure, respectively; ρ is material density; p denotes the loading vector consisting of distributed loads in the axial, tangential, and normal directions; coordinates z1 and z2 (z1 < z2 ) represent the axial coordinates of the two ends of the thin-walled structure and σ indicates the strain vector imposed at the ends
These facts proved that the proposed model, with a set of sectional deformation modes derived from a cantilevered structure, could accurately reproduce three-dimensional behaviors of thin-walled structures with their two ends fixed
Summary
Received: 10 September 2018; Accepted: 1 October 2018; Published: 9 October 2018. Featured Application: The simplified approach, along with the derived one-dimensional higher-order model, possesses efficiency and accuracy which makes it an alternative to the more sophisticated shell finite elements in the numerical analyses of thin-walled structures.
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