Geometric-material analogy for multiscale modelling of twisted plates

It is well known that the macroscopic behaviour of many engineering materials is strongly affected by the role of underlying microstructure. Currently though, mathematical expressions linking behaviour of large scale structures to the geometry of their microscopic structure are largely lacking. In this respect, establishing quantitative links across different material lengthscales may offer new pathways for engineering design. In the present work an analogy between cross sectional geometrical properties, representing macrostructure, and a material length parameter, representing microstructure, is presented. The analogy is established through the study of a thin plate subject to axial loading undergoing finite displacements from two alternative perspectives. First, we consider a thin elastic plate with a pretwist about the loading axis where a warping term is introduced accounting for the out-of-plane deformation of the cross section. The coupled governing differential equations and the corresponding coupled boundary conditions are explicitly derived employing a classical structural mechanics approach utilising an energy variational statement. Secondly, an axially loaded thin flat plate (i.e. with no pretwist) is studied with strain gradient elasticity theory incorporating only one material length parameter representing the microstructure, in addition to the two classical Lamé stiffness constants. The ensuing analogy emerges by comparison of the governing equations of the two formulations which shows a mathematical expression can be identified, which incorporates both geometric and material length variables, that formalises the link between microscale and macroscale. This mathematical expression, which constitutes the kernel of the proposed multiscale approach, admits a twofold interpretation depending on the assumed independent variable. On the one hand, the proposed multiscale modelling approach suggests that a plate with complex global geometry can be substituted by a structurally - equivalent, flat plate with constitutive relations given by a non - local, strain gradient theory. On the other hand, the material length parameter can be interpreted on a physical basis because for the first time it has been identified as a known function of geometrical features of the structure through simple algebraic relationships for various cross sectional profiles

Re-submission: Supplementary material from "The role of symmetry in the post-buckling behaviour of structures"

Re-submission: Supplementary material from "The role of symmetry in the post-buckling behaviour of structures

Three-dimensional effects influencing failure in bend-free, variable stiffness composite pressure vessels

Pressure vessels enable liquids and gases to be stored and transported safely, finding pervasive use in many industries. These types of structure can be manufactured into many different shapes and from various materials to satisfy the requirements of their specific applications. Maximum allowable pressure is an important factor that should be considered carefully in the design process. Bend-free pressure vessels, that are enabled by variable stiffness composite designs, can even out in-plane stress distributions in the through-thickness direction thereby increasing overall load carrying capacity often accompanied by significant weight reduction. Bend-free composite vessels can therefore be considered to be possible candidates for the next generation of pressure vessels and therefore it is important to study their failure performance, often driven by safety reasons. In this study, the maximum allowable internal pressure is determined for bend-free ellipsoidal pressure vessels exploiting variable stiffness properties, using first-ply failure based on both Tsai-Wu and the recently proposed three-dimensional invariant-based failure criteria with performance subsequently compared against conventional constant stiffness, composite vessels. Parametric studies are then performed to provide physical insight and also to evaluate the effect of various material properties on the difference in failure load prediction found by these criteria

Efficient strong unified formulation for stress analysis of non-prismatic beam structures

The Unified Formulation (UF) has gained attention as a powerful tool for efficient design of structural components. Due to the inherent flexibility of its kinematics representation, arbitrary shape functions can be selected in different dimensions to achieve a high‐fidelity characterisation of structural response under load. Despite this merit, the classical isoparametric description of UF limits the application to prismatic structures. The weak‐form anisoparametric approach adopted to overcome this limitation in a recent work by Patni et al. proves to be versatile yet computationally challenging owing to the expensive computation of its UF stiffness matrix by means of full volume integrals. We propose a strong‐form anisoparametric UF (SUF) based on the Serendipity Lagrange Expansion (SLE) cross‐sectional finite element and differential quadrature beam element. The main objective of the SUF is to achieve an efficient computation of the UF stiffness matrix by restricting Gauss operations to the variable cross‐sections of non‐prismatic structures in a discrete sense, thus eliminating the need for full volume integrals. When assessed against weak‐form based UF, ABAQUS FE and analytical solutions, the static analysis of non‐prismatic beam‐like structures under different loads by the SUF is shown to be accurate, numerically stable, and computationally more efficient than state‐of‐the‐art method

Variable stiffness composite beams subject to non-uniformly distributed loads: An analytical solution

An analytical solution is obtained for the 3D static deflection of variable stiffness composite beams subject to non-uniformly distributed loads. Governing differential equations with variable coefficients, reflecting the spatially variable stiffness properties, are presented in which four degrees of freedom are fully coupled. The general analytical solution in integral form is derived and closed-form expressions obtained using series expansion approximations. The static deflection of a number of variable stiffness composite beams that can be made by fibre steering are considered with various stacking sequences. The results obtained from the proposed method are validated against numerical results from the Chebyshev collocation method and excellent agreement is observed between the two. While the proposed methodology is applicable for variable stiffness composite beams with arbitrary span-wise variation of properties, it is also an efficient approach for capturing the complicated 3D static deflection of variable stiffness composite beams subject to non-uniformly distributed loads

A variable-topology morphing composite cylindrical lattice

Morphing composite structures are of significant interest due to the fact that they exhibit superior mass‐to‐ stiffness ratios and a large degree of tailorability in comparison to traditional materials and structures. One such morphing composite structure is the multistable composite cylindrical lattice. Current work introduces a novel variable‐topology morphing mechanism to it through the use of both permanent magnets and electro-magnets. By replacing a set of mechanical fasteners from the central intersection of the lattice strips with a bespoke variable‐topology mechanism introduces a controllable and replicable semi‐autonomous means for topology morphing. The variable‐topology mechanism allows the structure to transition from being a linear deployment actuator to one that deploys along a curved path, without need for external mechanical input. The behaviour of both the variable‐topology mechanism and the topology‐changing cylindrical lattice are thoroughly characterised through a combination of mechanical and virtual tests

Morphing lattice boom for space applications

Structures used in space applications demand the highest levels of stiffness for their mass whilst also performing in a hostile environment. To partly address these requirements and so as to also pack efficiently for stowage during launch we propose a new type of compact telescopic morphing lattice space boom. This boom stows within a 1U CubeSat volume and is lightweight being only 0.4 kg. The boom has a total length of 2 m in its deployed state which is 20 times its stowed height. The device comprises two multi-stable cylindrical composite lattices that are joined telescopically. These lattices nest inside one another in the stowed configuration, with the objective of improving packaging efficiency. Notably, prestress and lamina orientation are used to smoothly change shape from being compact when stowed to being extended when deployed. The lattices in the boom have been designed to maximise deployment force and to be self-deploying by tuning manufacturing parameters. As a result, only a small, lightweight mechanism is required to regulate deployment speed of the lattice boom. By reversing its direction, this mechanism can be used to retract the lattice boom to its stowed configuration, thereby enabling two-way reconfigurability

Closed-form solutions for the coupled deflection of anisotropic euler–bernoulli composite beams with arbitrary boundary conditions

The fully anisotropic response of composite beams is an important consideration in diverse applications including aeroelastic responses of helicopter rotor and wind turbine blades. Our goal is to present exact analytical solutions for the first time for coupled deflection of Euler–Bernoulli composite beams. Towards this goal, two approaches are proposed: (1) obtaining the exact analytical solutions directly from the governing equations of Euler–Bernoulli composite beams and (2) extraction of the solutions from Timoshenko composite beam solutions. For the direct solution approach, based on Euler–Bernoulli theory, new variationally-consistent field equations are obtained, in which four degrees of freedom, i.e. in-plane bending, out-of-plane bending, twist and axial elongation are fully coupled. By expressing the coupled system of differential equations in a compact matrix form, a novel expression for the eccentricity of neutral axes from the midplane, as well as the shift in shear centre from the centre of beam, is obtained. This eccentricity matrix serves to decouple the bending in the two principal directions from in-plane and twist deformations. Then, the general closed-form analytical solutions for the decoupled system are derived simply using direct integration. Additionally, the analogous closed-form analytical solutions are retrieved from the previously obtained Timoshenko composite beam solution and it is proven that they are identical to those obtained from the current direct approach for conditions where Euler–Bernoulli beam theory apply. To study the effects of anisotropy, numerical results are obtained for a number of examples with different composite stacking sequences showing various coupled behaviours. The results are compared against the Chebyshev collocation method as well as against less comprehensive analytical solutions available in the literature, noting that excellent agreement is observed, where expected. The present exact solutions can serve as benchmark problems for assessing the accuracy and convergence of various analytical and numerical method

Thermal-mechanical optimization of folded core sandwich panels for thermal protection systems of space vehicles

The integrated thermal protection system (ITPS) is a complicated system that addresses both mechanical and thermal considerations. An M-pattern folded core sandwich panel packedwith low-density insulation material provides inherently lowmass for a potential ITPS panel. Herein, we identify the most influential geometric parameters and establish a viable, computationally efficient optimization procedure. Variables considered for optimization are geometric dimensions of the ITPS, while temperature and deflection are taken as constraints. A one-dimensional (1D) thermal model based on a modified form of the rule of mixtures was established, while a three-dimensional (3D) model was adopted for linear static analyses. Parametric models were generated to facilitate a design of experiment (DOE) study, and approximate models using radial basis functions were obtained to carry out the optimization process. Sensitivity studies were first conducted to investigate the effect of geometric parameters on the ITPS responses. Then optimizations were performed for both thermal and thermal-mechanical constraints. The results show that the simplified 1D thermal model is able to predict temperature through the ITPS thickness satisfactorily. The combined optimization strategy evidently improves the computational efficiency of the design process showing it can be used for initial design of folded core ITPS

Morphing of symmetric cross-ply cylindrical shells by minimising the brazier moment: Optimised hinge folding

Aerospace and industries where both localised compliance and weight savings play a central role in design can benefit from using flexible hinges. These morphing structures use no mechanical hinges for folding. They fold by exploiting the limit point, i.e. the Brazier moment, of a geometrically nonlinear structural response characteristic of thin-walled beams under bending. Therefore, a smaller Brazier moment induces smaller non-classical stresses in the hinge during folding. Two aspects make cross-ply laminates attractive for designing flexible hinges. Firstly, the difference between the Brazier moment of an optimal symmetric generic laminate and that of an optimal symmetric cross-ply is relatively small. Secondly, cross-ply laminates do not exhibit extension-shear or bend-twist couplings which can induce complex deformations which can present challenges during design, especially considering that available analytical solutions of the Brazier moment neglect their effects. Driven by these premises, this work contributes to the preliminary design of flexible hinges by offering an analytical solution of the optimum symmetric cross-ply laminate for minimising the Brazier moment, which is subsequently validated through geometrically nonlinear finite element analysis. Moreover, this work provides insights into the prediction of the folding load considering the effects of local buckling instabilities