A multi-scale approach for the optimum design of sandwich plates with honeycomb core. Part I: homogenisation of core properties

This work deals with the problem of the optimum design of a sandwich panel. The design process is based on a general two-level optimisation strategy involving different scales: the meso-scale for both the unit cell of the core and the constitutive layer of the laminated skins and the macro-scale for the whole panel. Concerning the meso-scale of the honeycomb core, an appropriate model of the unit cell able to properly provide its effective elastic properties (to be used at the macro-scale) must be conceived. To this purpose, in this first paper, we present the numerical homogenisation technique as well as the related finite element model of the unit cell which makes use of solid elements instead of the usual shell ones. A numerical study to determine the effective properties of the honeycomb along with a comparison with existing models and a sensitive analysis in terms of the geometric parameters of the unit cell have been conducted. Numerical results show that shell-based models are no longer adapted to evaluate the core properties, mostly in the context of an optimisation procedure where the parameters of the unit cell can get values that go beyond the limits imposed by a 2D model

Buckling strength improvements for Fibre Metal Laminates using thin-ply tailoring

The buckling response and load carrying capacity of thin-walled open cross-section profiles made of Fibre Metal Laminates, subjected to static axial compression loading are considered. These include thin-walled Z-shape and channel cross-section profiles adopting a 3/2 FML lay-up design, made of 3 aluminium layers. The objective of the investigation is the comparison of standard thickness Fibre Reinforced Plastic layers versus thin-ply material technology. Whilst thin ply designs differ only by the layer thickness, they offer an exponential increase in stacking sequence design freedoms, allowing detrimental coupling effects to be eliminated. The benefit of different hybrid materials are also considered. The comparisons involve semi-analytical and finite element methods, which are validated against experimental investigations

Design of Meta-Materials Outside the Homogenization Limit Using Multiscale Analysis and Topology Optimization

The field of meta-materials engineering has largely expanded mechanical design possibilities over the last two decades; some notable design advances include the systematic engineering of negative Poisson\u27s ratio materials and functionally graded materials, materials designed for optimal electronic and thermo-mechanical performances, and the design of materials under uncertainty. With these innovations, the systematic engineering of materials for design-specific uses is becoming more common in industrial and military uses. The motivation for this body of research is the design of the shear beam for a non-pneumatic wheel. Previously, a design optimization of a finite element model of the non-pneumatic wheel was completed, where a linear elastic material was simulated in the shear beam to reduce hysteretic energy losses. As part of the optimization, a set of optimal orthotropic material properties and other geometric properties were identified for the shear beam. Given that no such natural linear elastic material exists, a meta-material can be engineered that meets these properties using the aforementioned tools. However, manufacturing constraints prevent the use of standard homogenization analysis and optimization tools in the engineering of the shear beam due to limitations in the accuracy of the homogenization process for thin materials. In this research, the more general volume averaging analysis is shown to be an accurate tool for meta-material analysis for engineering thin-layered materials. Given an accurate analysis method, several optimization formulations are proposed, and optimality conditions are derived to determine the most mathematically feasible and numerically reliable formulation for topology optimization of a material design problem using a continuous material interpolation over the design domain. This formulation is implemented to engineer meta-materials for problems using the volume averaging analysis, which includes the use of variable linking and the derivation of first-order design sensitivities to increase computational efficiency. Inspired by honeycomb materials, a new method of discretizing the material design domain into unit cells with non-simple connectivity is proposed as a way of increasing the solution space of the topology optimization problem. Finally, these methods are used in the meta-material design process to identify several candidate meta-material geometries from a polycarbonate base material for the shear layer of the non-pneumatic wheel; notable geometries include an `x\u27-like geometry, a bent column-like geometry identified previously as a bristle, and, remarkably, an auxetic honeycomb geometry. This is the first reported result demonstrating the auxetic honeycomb geometry to be a minimum weight structure in shear loading where a general topology optimization method was used

On the possible effective elasticity tensors of 2-dimensional and 3-dimensional printed materials

The set $GU_f$ of possible effective elastic tensors of composites built from two materials with elasticity tensors \BC_1>0 and \BC_2=0 comprising the set U=\{\BC_1,\BC_2\} and mixed in proportions $f$ and $1-f$ is partly characterized. The material with tensor \BC_2=0 corresponds to a material which is void. (For technical reasons \BC_2 is actually taken to be nonzero and we take the limit \BC_2\to 0). Specifically, recalling that $GU_f$ is completely characterized through minimums of sums of energies, involving a set of applied strains, and complementary energies, involving a set of applied stresses, we provide descriptions of microgeometries that in appropriate limits achieve the minimums in many cases. In these cases the calculation of the minimum is reduced to a finite dimensional minimization problem that can be done numerically. Each microgeometry consists of a union of walls in appropriate directions, where the material in the wall is an appropriate $p$-mode material, that is easily compliant to $p\leq 5$ independent applied strains, yet supports any stress in the orthogonal space. Thus the material can easily slip in certain directions along the walls. The region outside the walls contains "complementary Avellaneda material" which is a hierarchical laminate which minimizes the sum of complementary energies.Comment: 39 pages, 11 figure

Integrated analysis and design of thick composite structures for optimal passive damping characteristics

The development of novel composite mechanics for the analysis of damping in composite laminates and structures and the more significant results of this effort are summarized. Laminate mechanics based on piecewise continuous in-plane displacement fields are described that can represent both intralaminar stresses and interlaminar shear stresses and the associated effects on the stiffness and damping characteristics of a composite laminate. Among other features, the mechanics can accurately model the static and damped dynamic response of either thin or thick composite laminates, as well as, specialty laminates with embedded compliant damping layers. The discrete laminate damping theory is further incorporated into structural analysis methods. In this context, an exact semi-analytical method for the simulation of the damped dynamic response of composite plates was developed. A finite element based method and a specialty four-node plate element were also developed for the analysis of composite structures of variable shape and boundary conditions. Numerous evaluations and applications demonstrate the quality and superiority of the mechanics in predicting the damped dynamic characteristics of composite structures. Finally, additional development was focused on the development of optimal tailoring methods for the design of thick composite structures based on the developed analytical capability. Applications on composite plates illustrated the influence of composite mechanics in the optimal design of composites and the potential for significant deviations in the resultant designs when more simplified (classical) laminate theories are used

Optimization of Lay-Up Stacking for a Loaded-Carrying Slender Composite Beam

Many aircraft composite structures experiencing the high operational loads must have the specified mechanical stiffness to prevent some structural failure due to the inadmissible deformations. Usually, such parts are manufactured using composites with orthotropic symmetry, which provides the best combination of structural rigidity, strength, and weight. In this chapter, we consider a cantilevered long tube-like composite structure with varied cross-section that is manufactured by winding of glass fiber unidirectional tape. The operational loads include the bending forces and the distributed torques. To reduce the total strain energy and peak von Mises stress, the search of the best lay-up scheme and its angles is performed. The wall thickness, lay-up scheme, and the total number of layers for each modeled design are assumed as unchanged along the tube, whereas its mechanical properties are considered as homogenized and dependent on the lamina properties and lay-up scheme only. The search of the pseudo-optimal design includes the analysis of all moduli angular distributions for each lay-up stacking. The better solutions are then studied by using the finite element model of the structure for three most critical load scenarios. The choice of the most preferred design is made by discarding the solutions with sharply degraded structural rigidity at least at one load scenario

Stacking sequences in composite laminates through design optimization

AbstractComposites are experiencing a new era. The spatial resolution at which is to date possible to build up complex architectured microstructures through additive manufacturing-based and sintering of powder metals 3D printing techniques, as well as the recent improvements in both filament winding and automated fiber deposition processes, are opening new unforeseeable scenarios for applying optimization strategies to the design of high-performance structures and metamaterials that could previously be only theoretically conceived. Motivated by these new possibilities, the present work, by combining computational methods, analytical approaches and experimental analysis, shows how finite element Design Optimization algorithms can be ad hoc rewritten by identifying as design variables the orientation of the reinforcing fibers in each ply of a layered structure for redesigning fiber-reinforced composites exhibiting at the same time high stiffness and toughening, two features generally in competition each other. To highlight the flexibility and the effectiveness of the proposed strategy, after a brief recalling of the essential theoretical remarks and the implemented procedure, selected example applications are finally illustrated on laminated plates under different boundary conditions, cylindrical layered shells with varying curvature subjected to point loads and composite tubes made of carbon fiber-reinforced polymers, recently employed as structural components in advanced aerospace engineering applications

Topology optimization-guided stiffening of composites realized through Automated Fiber Placement

The paper proposes a mixed strain- and stress-based topology optimization method for designing the ideal geometry of carbon fibers in composite laminates subjected to either applied tractions or prescribed displacements. On the basis of standard micromechanical approaches, analytical elastic solutions for a single cell, assumed to be a Representative Volume Element (RVE), are ad hoc constructed by involving anisotropy induced by fiber orientation and volume fraction, also taking into account inter-laminar stresses and strains. The analytical solutions are then implemented in a Finite Element (FE) custom-made topology optimization-based procedure rewritten to have as output the best curves the reinforcing fibers have to draw in any composite laminate layer to maximize the overall panel stiffness or to minimize the elastic energy. To verify the effectiveness of the proposed strategy, different structures undergoing either in-plane or out-plane boundary conditions have been selected and theoretically investigated, determining the optimal fibers’ maps and showing the related results in comparison to standard sequences of alternate fibers disposition for the same composites. Two optimized panels were at the end actually produced using an innovative Automated Fiber Placement (AFP) machine and consolidating the materials by means of autoclave curing processes, in this way replicating the fiber paths obtained from theoretical outcomes. As a control, two corresponding composite structures were also built without employing the fiber optimization strategy. The panels have been tested in laboratory and the theoretical results have been compared with the experimental findings, showing a very good agreement with our predictions and confirming the capability of the proposed algorithm in suggesting the arrangement of the fibers to obtain enhanced mechanical performances. It is felt that the hybrid analytical-FE topology optimization strategy, in conjunction with the possibilities offered by AFP devices, could pave the way for a new generation of ultra-lightweight composites for aerospace, automotive and many industrial applications