Aerothermoelastic flutter analysis of variable angle tow composite laminated plates in supersonic flow

Fibre-reinforced polymers (FRP) are increasingly adopted in bridge structures to reduce their environmental impact, extend service life and save costs. These results are achieved thanks to the high stiffness and strength-to-weight ratios, the faster installation time and the superior resistance to environmental degradation of FRP composites compared to traditional building materials. In this work, we propose the use of composite laminates called Variable Angle Tow (VAT) in bridge structures. Unlike traditional laminates characterised by straight fibres, VAT laminates have fibre orientations that change pointwise across the structure, following curvilinear paths. This feature enhances the stiffness tailoring capabilities and allows for more optimised designs. In aerospace engineering, VAT composites have successfully tailored structural stiffness to improve linear elastic response, reduce buckling phenomena, and optimise postbuckling behaviour. However, VAT laminates have not yet been applied in civil structures. This work shows that using VAT composite laminates in a bridge girder improves buckling and postbuckling behaviours and increases overall stiffness. The benefits provided by VAT composite laminates to the structural performance of bridge girders are demonstrated through a parametric numerical study and a multi-objective optimisation. For different spans, results show that VAT laminates exhibit a buckling load up to 80% over traditional straight fibre laminates, with equal or lower deflections and without adding extra material, opening new design scenarios for bridge structures.

Multi-level intelligent design of variable angle tow laminates via image-driven method

Thermo-mechanical buckling analysis of symmetric VAT composite laminates with temperature-dependent material properties

Variable-angle tow describes fibers in a composite lamina that have been steered curvilinearly. In doing so, substantially enlarged freedom for stiffness tailoring of composite laminates is enabled. Variable-angle tow composite structures have been shown to have improved buckling and postbuckling load-carrying capability when compared to straight fiber composites. However, their structural analysis and optimal design is more computationally expensive due to the exponential increase in number of variables associated with spatially varying planar fiber orientations in addition to stacking sequence considerations. In this work, an efficient two-level optimization framework using lamination parameters as design variables has been enhanced and generalized to the design of variable-angle tow plates. New explicit stiffness matrices are found in terms of component material invariants and lamination parameters. The convex hull property of B-splines is exploited to ensure pointwise feasibility of lamination parameters. In addition, a set of new explicit closed-form expressions defines the feasible region of two in-plane and two out-of-plane lamination parameters, which are used for the design of orthotropic laminates. Finally, numerical examples of plates under compression loading with different boundary conditions and aspect ratios are investigated. Reliable optimal solutions demonstrate the robustness and computational efficiency of the proposed optimization methodology.

Variable Angle Tows (VAT) composite materials can effectively transfer major stresses from the interior region to the edges through in-plane load redistribution, thereby significantly enhancing their structural performance. Therefore, correct handling of boundary conditions is crucial in analyzing VAT structures. Considering that most practical engineering cases involve non-ideal or non-classical boundary support, this paper proposes an efficient method to address the nonlinear thermal flutter problem of elastic supported VAT curved panels in supersonic airflow. Assuming the fiber orientation angle varies in four different ways along the x-direction, the basic equations are established based on the von Kármán large deformation plate theory and the first-order piston theory. The generalized Galerkin method, capable of handling arbitrary elastic boundary constraints, is used to solve the problem in the space domain, while the Runge-Kutta method is applied in the time domain. Numerical examples illustrate how elastically restrained conditions, fiber orientation angles, height-rise ratio, and thermal loads, along with aerodynamic pressure, influence flutter responses of VAT panels. The presented method can be used for the aeroelastic stability design of VAT curved panels under arbitrary boundary conditions.

Static and dynamic analysis of two-phase peridynamic one-dimensional systems is thoroughly investigated in this paper for various boundary conditions by exact and numerical approaches. Such a nonlocal study concerns the axial or torsional responses of two-phase peridynamic rods or the behavior of a two-phase peridynamic string. For a normalized exponential kernel, the integro-differential equation of the two-phase peridynamic problem can be converted as a linear higher-order differential equation with constant coefficients. Exact static solutions of fixed–fixed and fixed–free two-phase peridynamic axial rod (TPPAR) under uniform distributed loading and concentrated force are analytically derived. It is shown that the pure peridynamic rod problem can be ill-posed due to a conflict between the natural boundary condition and the peridynamic constitutive boundary condition. The two-phase peridynamic problem may be justified from physical arguments, and is also seen as a regularized peridynamic problem. The exact eigen-frequencies of the two-phase peridynamic rods are also analytically obtained for various boundary conditions, including fixed–free, fixed–fixed or free–free boundary conditions. These theoretical approaches are corroborated by numerical investigations based on Finite Difference Method (FDM), Finite Element Method (FEM), exact FEM and variational iterative methods. Two FDM schemes are presented for the statics and the vibration of two-phase peridynamic rods, with convergence orders of 1 and 2, respectively. Moreover, three different FE procedures are proposed as: (1) FEM for direct solving the integro-differential equations of two-phase peridynamic one-dimensional system, (2) FEM for discretizing the pure differential equations, and (3) Exact FEM to obtain both the exact stiffness matrix and exact dynamic stiffness matrix of two-phase peridynamic one-dimensional system, based on Eisenberger’s methodology. The order of convergence for the first and the second proposed FEM is equal to 2 and 4, according to the type of selected finite elements. Moreover, the third proposed FEM based on the exact shape function of the peridynamic problem gives the exact solution from one single FEM element. In addition, the variational iterative method of Stodola–Vianello is successfully applied to the two-phase peridynamic eigenvalue problems.

A geometrical nonlinear analysis of a symmetric, variable angle tow (VAT), composite plate structure under inplane shear load is investigated in this work. The nonlinear vonKarman governing differential equations (GDEs) based on stress function and displacement function are derived for postbuckling analysis of symmetric VAT plate structures. A numerical methodology based on the differential quadrature method (DQM) is developed for solving the GDEs of VAT plates. The methodology is applied to solve the postbuckling problem of VAT plates with linear fibre angle orientations under simply supported plate boundary conditions. To show the accuracy and robustness of DQM, results are compared with commercial finite element analysis. The postbuckling behaviour of VAT plates under positive and negative shear is studied for different VAT fibre orientations, aspect ratios and their performance is compared with straight fibre composites. In addition, the influence of the direction of shear on the postbuckling behavior of VAT plates under axial compression is studied.

A unified modeling approach for rotating flexible shaft-disk systems with general boundary and coupling conditions

Postbuckling analysis of variable angle tow composite plates

An analysis of the flowfield about a circular-cylinder mounted normal to a flat plate in supersonic flow is presented. The subject flowfield was generated utilizing Navier-Stokes (NS) Computational Fluid Dynamics (CFD) techniques as embodied in a developmental version of a proprietary finite-volume NS flow solver. The primary aim of the study was to provide a reasonable degree of validation relative to the code's ability to correctly predict protuberanceinduced interference flowfield topologies. results of References 1 and 2. A summary of the wind tunnel test section flow conditions for the subject wind tunnel tests is provided below:

Nonlinear postbuckling of symmetric S-FGM plates resting on elastic foundations using higher order shear deformation plate theory in thermal environments

A simply-supported multi-walled carbon nanotube (MWCNT) is considered. Its vibrations will be studied in a cylindrical coordinate system. The elastic constants in Hooke's law depend on the CNT wall diameter, which is why each wall has its own elastic constants. CNT vibrations are described by the Sanders-Koiter shell theory. To derive partial differential equations (PDE) describing self-induced variations, a variational approach is used. The PDEs of vibrations are derived with respect to three projections of displacements. The model takes into account the Van der Waals forces between CNT walls. The three projections of displacements are expanded in basis functions. It was not possible to select the basis functions satisfying both geometric and natural boundary conditions. Therefore, selected are the basis functions that satisfy only geometric boundary conditions. To obtain a linear dynamic system with a finite number of degrees of freedom, the method of weighted residuals is used. To derive the basic relations of the method of weighted residuals, methods of variational calculus are used. The vibrational eigenfrequencies of single-walled (SW) CNTs are analyzed depending on the number of waves in the circumferential direction. With the number of waves in the circumferential direction from 2 to 4, the vibrational eigenfrequencies of CNTs are minimal. These numbers are smaller than those for the vibrational eigenfrequencies of engineering shells. Anisotropic models of tripple-walled (TW) CNTs were investigated. In their eigenforms, there is interaction between the basis functions and different numbers of waves in the longitudinal direction. This phenomenon was not observed in the isotropic CNT model. The appearance of such vibrations is a consequence of structural anisotropy.

Natural frequency analysis of imperfect GNPRN conical shell, cylindrical shell, and annular plate structures resting on Winkler-Pasternak Foundations under arbitrary boundary conditions

Observation and evolution of chaos for a cantilever plate in supersonic flow

Buckling analysis and optimisation of variable angle tow composite plates