Vibration and buckling of open TWBs with local weakening

Free vibration and Ljapounov stability of compressed open thin-walled beams with a cross-section reduction are studied by a in-house finite differences numerical code, based on a refined direct beam model and allowing for investigating elastic stability of non-trivial equilibrium paths in a dynamic setting. The benchmark is a beam with doubly symmetric cross-section and non-zero warping rigidity, under free, semi-, and fully restrained warping at its ends. In all cases, the results of the direct model are compared to finite element and/or experimental ones. The reduction in the cross-section rigidity induces a weakening that may model a local damage; thus, the present investigation may be useful with an outlook to damage monitoring and identification

Perturbation damage indicators based on complex modes

The papers focusing on dynamic identification of structural damages usually rely on the comparison of two or more responses of the structure; the measure of damage is related to the differences of the vibration signals. Almost all literature methods assume damping proportionality to mass and stiffness; however, this is acceptable for new, undamaged structures, but not for existing, potentially damaged structures, especially when localised damages occur. It is well-known that in non-proportionally damped systems the modes are no longer the same of the undamped system: thus, some authors proposed to use modal complexity as a damage indicator. This contribution presents a perturbation approach that can easily reveal such a modal complexity

Rotor blades as curved, twisted and tapered beam-like structures subjected to large deflections

Non-prismatic beam-like structures are widespread in many engineering and science applications. Important examples include the rotor blades of wind turbines and helicopters. Their mechanical behaviour can be simulated using 3D beam models, which are computationally efficient, accurate and explicitly consider such structures’ main geometric features, the large deflection of their reference centre-line and 3D warping of their transverse cross-sections. This paper proposes a mathematical model for such structures. A variational approach and the smallness of the warping and strain fields are exploited to obtain the model. Analytical and numerical results obtained with the proposed modelling approach are presented and compared to those from nonlinear 3DFEM simulations

On proper applications of Galërkin’s approach in structural mechanics courses

An incautious use of the well-known Galërkin’s technique to find approximate solutions of a differential problem may lead to apparently wrong results. Examples are based on an inverse approach to investigate buckling of compressed axisymmetric circular plates, a common subject in courses on mechanics of structures and stability of structural elements. We discuss how a mistake may originate and show how it is possible to recover the expected results, thus providing a means for the students to cross-check their outputs

Buckling of circular plates with functional grading in two directions

This short note considers thin circular plates, functionally graded in both axial and transverse directions and loaded in compression on the middle plane by a uniform axisymmetric load. The functional grading is based on recent literature on the subject and we deal with a direct problem for buckling, i.e., given the geometry of the plate and its constitutive properties, the critical load multiplier and the buckling mode are determined by a usual non-triviality condition. Original expressions are found in a nearly closed form and show that suitable functional grading, actually achievable in practice, may lead to gentle solutions. Numerical examples, physical interpretations and comments are provided

Perturbations for vibration of nano-beams of local/nonlocal mixture

Here we extend the perturbation approach, previously presented in the literature for Eringen’s two-phase local/nonlocal mixture model, to free vibration of purely flexible beams. In particular, we expand the eigenvalues and the eigenvectors into power series of the fraction coefficient of the non-local material response up to 2nd order. We show that the family of 0th order bending couples satisfy the natural and essential boundary conditions of the 1st order; hence, the 1st order solution can conveniently be constructed using the eigenspace of the 0th order with no necessity of additional conditions. We obtain the condition of solvability that provides the incremental eigenvalue in closed form. We further demonstrate that the 1st order increment of the eigenvalue is always negative, providing the well-known softening effect of long-range interactions among the material points of a continuum modelled with Eringen’s theory. We examine a simply supported beam as a benchmark problem and present the incremental eigenvalues in closed form. © 2023, Association of American Publishers. All rights reserved.2-s2.0-8515266294

General theory for plane extensible elastica with arbitrary undeformed shape

A general expression for the strain energy of a homogeneous, isotropic, plane extensible elastica with an arbitrary undeformed configuration is derived. This expression appears to be suitable for one-dimensional models of polymers or vesicles, the natural configuration of which is characterized by locally changing curvature. In a linear setting, we derive the macroscopic stress–strain relations, providing an universal criterion for the neutral curve location. In this respect, we further demonstrate that the neutral curve existence constitutes the fundamental requirement for the conformational dynamics of any inextensbile biological filament

A direct one-dimensional beam model for the flexural-torsional buckling of thin-walled beams

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Artificial dataset generation to enhance the design exploration of residential buildings through data-informed energy load forecasting models

This study aims to assist urban planners and building designers in taking informed decisions based on energy performance – simulating a real-world urban development scenario – using limited computational resources. In particular, this paper proposes a new approach that integrates existing studies on building loads forecasting by using a Generative Adversarial Network (GAN) generated dataset based on significant geometrical parameters. This overcomes the needs for large datasets – often difficult to access.The results demonstrate that the data-driven approaches have addressed the buildings' load predictions with a reasonable accuracy while significantly reducing the calculation time required

Modulated linear dynamics of nanobeams accounting for higher gradient effects

We present some numerical results for the linear dynamics of nanobeams modulated by an axial force, basing on a recent proposal of literature that encompasses both the standard nonlocal elasticity, according to Eringen, and second-order strain elasticity. Three different possibilities for the elastic potential energy provide different responses that highlight the contributions of nonlocality and strain gradient, plus their combination. An axial force affects the linear stationary dynamics of such nanobeams, inducing suitable variation of the natural angular frequencies for benchmark cases, until static buckling occurs when the natural angular frequency vanishes. Effects of the various elastic potentials on this modulation are investigated and thoroughly commented