An axiomatic/asymptotic evaluation of best theories for isotropic metallic and functionally graded plates employing non-polynomic functions

This paper presents Best Theory Diagrams (BTDs) constructed from various non-polynomial terms to identify best plate theories for metallic and functionally graded plates. The BTD is a curve that provides the minimum number of unknown variables necessary to obtain a given accuracy or the best accuracy given by a given number of unknown variables. The plate theories that belong to the BTD have been obtained using the Axiomatic/Asymptotic Method (AAM). The different plate theories reported are implemented by using the Carrera Unified Formulation (CUF). Navier-type solutions have been obtained for the case of simply supported plates loaded by a bisinusoidal transverse pressure with different length-to-thickness ratios. The BTDs built from non-polynomial functions are compared with BTDs using Maclaurin expansions. The results suggest that the plate models obtained from the BTD using nonpolynomial terms can improve the accuracy obtained from Maclaurin expansions for a given number of unknown variables of the displacement field

A variable kinematic one-dimensional model for aeroelasticity and dynamic analysis of multi-layered rotors

Flutter is one of the most known instability phenomena. This condition occurs when a given structure exhibits sustained, harmonic oscillations, sometimes leading to catastrophic events. The prediction of flutter represents a crucial point for a correct and safe design. When fluid structure interactions produce dynamic instability, flutter analyses require accurate descriptions of body deformations and aerodynamic loads. To this end, aerodynamic theories have been coupled with structural models to develop aeroelastic analysis tools, whose reliability is the results of a trade-off between the accuracy and the computational efficiency. From a computational point of view, the most efficient formulation is based on the 1D assumption, where the problem is reduced to a set of variables that only depends on the beam-axis coordinate. Besides the well-known classical beam theories, several refined kinematic models have been proposed, to study the stability of rotating blades and shafts. However, when these structures are highly deformable or the material distribution involves non-classical structural couplings, 2D and 3D solutions are still required. Within this work, we propose an advanced 1D formulation to analyse the stability of rotating structures. The higher-order beam theories are obtained using the Carrera Unified Formulation (CUF), which allows to derive, at least theoretically, an infinite number of kinematic models. The Equations of Motion (EoM) for shafts and blades include the Coriolis term and the centrifugal effects (spin softening and geometrical stiffening). For the subsonic flow regime, aerodynamic loads are defined following the unsteady strip theories proposed by Theodorsen and Loewy. For the supersonic regime, the linear Piston theory is extended to structures rotating in compressed air flow. The Finite Element Method (FEM) is used to solve the weak form of the EoM. Firstly, to evaluate the accuracy of 1D CUF elements, static and free-vibration analysis are carried out on compact and thin-walled structures of isotropic, orthotropic and functionally graded materials. Then, higher-order elements are used to study the dynamics of laminated shafts, thin cylinders, discs and blades, which rotate about the longitudinal and transverse axis. Results show the improved performance of the 1D CUF theories compared to 2D and 3D solutions. In order to evaluate the proposed aeroelastic formulation, we test different wing configurations, including thin-walled box beams. The effects of the sweep angle and the lamination scheme on flutter conditions are evaluated, and results are compared with plate solutions, experimental tests and aeroelastic analysis carried out with the Doublet Lattice Method (DLM). Moreover, comparisons between Theodorsen and Loewy aerodynamic theories are presented for a realistic rotary-wing model. In the last numerical examples, the linear Piston Theory is used to describe the dynamics of thin plates with different aspect-ratio surrounded by compressed air. For this cases, results are compared with an existing solution based on a non-linear plate theory

C0 Layerwise Model with Fixed Degrees of Freedom and Variable In- and Out-of-Plane Kinematics by Strain Energy Updating Technique

Physically based zigzag models have the merit of giving accurate stress predictions for laminates and sandwiches keeping fixed the functional degrees of freedom, though at the expense of the introduction of their derivatives. In the present paper, a technique that enables deleting these derivatives is developed. The objective is finding a priori corrections of displacements, which make the energy of the model with all the derivatives neglected equivalent to that of its initial counterpart model containing all the derivatives. Numerical applications show that this technique can obtain accurate results, even for strongly asymmetrical lay-ups, keeping low the computational cost

Smart passive adaptive control of laminated composite plates (through optimisation of fibre orientation)

In the classical laminate plate theory for composite materials, it is assumed that the laminate is thin compared to its lateral dimensions and straight lines normal to the middle surface remain straight and normal to the surface after deformation. As a result, the induced twist which is due to the transverse shear stresses and strains are neglected. Also, this induced twist was considered as an unwanted displacement and hence was ignored. However, in certain cases this induced twist would not be redundant and can be a useful displacement to control the behaviour of the composite structure passively. In order to use this induced twist, there is a need for a modified model to predict the behaviour of laminated composites. A composite normally consists of two materials; matrix and fibres. Fibres can be embedded in different orientations in composite lay-ups. In this research, laminated composite models subject to transfer shear effect are studied. A semi analytical model based on Newton-Kantorovich-Quadrature Method is proposed. The presented model can estimate the induced twist displacement accurately. Unlike other semi analytical model, the new model is able to solve out of plane loads as well as in plane loads. It is important to mention that the constitutive equations of the composite materials (and as a result the induced twist) are determined by the orientation of fibres in laminae. The orientation of composite fibres can be optimised for specific load cases, such as longitudinal and in-plane loading. However, the methodologies utilised in these studies cannot be used for general analysis such as out of plane loading problems. This research presents a model whereby the thickness of laminated composite plates is minimised (for a desirable twist angle) by optimising the fibre orientations for different load cases. In the proposed model, the effect of transverse shear is considered. Simulated annealing (SA), which is a type of stochastic optimisation method, is used to search for the optimal design. This optimisation algorithm is not based on the starting point and it can escape from the local optimum points. In accordance with the annealing process where temperature decreases gradually, this algorithm converges to the global minimum. In this research, the Tsai-Wu failure criterion for composite laminate is chosen which is operationally simple and readily amenable to computational procedures. In addition, this criterion shows the difference between tensile and compressive strengths, through its linear terms. The numerical results are obtained and compared to the experimental data to validate the methodology. It is shown that there is a good agreement between finite element and experimental results. Also, results of the proposed simulated annealing optimisation model are compared to the outcomes from previous research with specific loading where the validity of the model is investigated

A refined sin hyperbolic shear deformation theory for sandwich FG plates by enhanced meshfree with new correlation function

The moving Kriging interpolation-based (MKI) meshfree method is extended to mechanical behavior analysis of isotropic and sandwich functionally graded material plates. The MKI meshfree method, which is free of shear correction factors effect in plate analysis, is further enhanced by introducing a new multi-quadric correlation function, eliminating drawbacks of its conventional form, gaining accurate solution. In this paper, a new refined sin hyperbolic shear deformation plate theory (N-RSHSDT) is introduced for plate kinematics. The present theory gives rise to four governing equations only, and achieves the sin hyperbolic distribution of the transverse shear strains through the plate thickness. To show the accuracy and effectiveness of the developed method, numerical experiments are performed for both isotropic and sandwich composite plates

A C0 zig-zag model for the analysis of angle-ply composite thick plates

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