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Design of lightweight structures

Novel manufacturing processes and new materials enable designs with variable stiffness considerably widened the design space and tailoring potential for many engineering applications.

I currently investigate novel design options, optimized to take into account manufacturing constraints, and structural constraints such as linear buckling, post-buckling, dynamic constraints, aeroelastic constraints, and desired morphing properties under nonlinear deformation.

Novel numerical techniques and formulation based on semi-analytical methods, meshless methods and conventional finite elements are developed and applied to enable achieving these advanced optimization frameworks.

Variable-angle filament-wound (VAFW) cylinders

Novel designs named variable-angle filament-wound (VAFW) cylinders are proposed, combining the tailoring capabilities of variable stiffness structures with very efficient manufacturing possibilities achieved with filament winding. In the study of Zhihua et al. we investigated reliability-based VAFW designs. The reference is given below and available with open access.

Zhihua Wang, José Humberto S. Almeida Jr., Luc St-Pierre, Zhonglai Wang, Saullo G. P. Castro. "Reliability-based buckling optimization with an accelerated Kriging metamodel for filament-wound variable angle tow composite cylinders". Composite Structures, Vol. 254, 2020. 10.1016/j.compstruct.2020.112821And some of the proposed designs are shown below.

Variable stiffness using 8 regions.

Variable stiffness using linear variation of the filament winding angle.

Variable stiffness using second-order variation of the filament winding angle.

In the study of Almeida Jr. et al. we covered the design, modeling, optimization, manufacturing and testing of variable-angle filament-wound cylinders. With the geometric imperfections characterized as per Castro et al. The two references are listed below, and available with open access.

José Humberto S. Almeida Jr., Luc St-Pierre, Zhihua Wang, Marcelo L. Ribeiro, Volnei Tita, Sandro C. Amico, Saullo G. P. Castro. "Design, modeling, optimization, manufacturing and testing of variable-angle filament-wound cylinders". Composites Part B, 2021. 10.1016/j.compositesb.2021.109224Castro, S. G. P., Almeida, J. H. S., Jr., St-Pierre, L., & Wang, Z. "Measuring geometric imperfections of variable-angle filament-wound cylinders with a simple digital image correlation setup". Composite Structures, 2021. 10.1016/j.compstruct.2021.114497

Variable angle-tow laminated composites

Here it is shown the overlaps created by the disposal of variable angle tows with constant width after progressive shifts along the y axis. Note the variation of \varphi along x.

Note the complex shape of the overlapping regions when two variable angle tow plies are stacked together.

Virtually-manufactured models vs. simplified models

Vertonghen and Castro investigated discrete versus smeared modelling techniques for variable-angle tow laminates, with variable stiffness properties and a thickness distribution that is nonlinearly coupled with the fiber steering.

Virtual manufacturing methods used to build as-manufactured finite element and semi-analytical models. Such models are hard to create, ideal to represent local manufacturing features such as gaps and overlaps, and to capture local responses such as strain/stress concentration, detect resin-reach regions and ultimately enable accurate strength predictions.

Simplified model using smeared thickness distribution. Such model is much simpler to create, ideal for precise stiffness representation and global responses such as global displacements, aeroelastic behavior, buckling, vibration, structure-borne noise emission and so forth.

Reliability-based design and optimization

Non-deterministic design and optimization considering stochastic variations of material properties, load and boundary conditions and manufacturing parameters.

This graphical abstract illustrates a study applying an accelerated Kriging metamodelling to below depicts an RBDO design of filament-wound cylinders.

Characterization of Geometric Imperfections

The imperfection signature created by different manufacturing processes has direct effect on the structural performance of imperfections-sensitive structures, such as unstiffened cylindrical shells.

A recent study in my lab showed how to use a simple digital image correlation (DIC) experimental setup to characterize the mid-surface and thickness imperfection of variable-angle filament-would (VAFW) cylinders. The figure below illustrates one of the cylinders that were used (VAFW8-3) and its corresponding imperfection signature. All this data is publicly available in two data sets: raw DIC data, and reconstructed imperfection signatures.

The cylinder topography is obtained using digital image correlation (DIC), and a series of six optimization steps are used to stitch the geometric imperfections in a reconstructed 3D pattern.

reconstruction 1/6

reconstruction 3/6

reconstruction 5/6

reconstruction 2/6

reconstruction 4/6

reconstruction 6/6

Meshless / meshfree methods applied in aerospace engineering

Meshless methods coupled with finite elements for fluid-structure interaction

The example below shows a flexible beam splashing into water. The fluid is modeled using particles, allowing abrupt changes of the fluid surface and boundary conditions, whereas the beam is represented with geometrically nonlinear finite elements. The method I am developing allows coupling with any finite elements framework.

Here, an aircraft ditching in a 3D simulation using 5.8 million particles.

Application of meshless methods to stability of thin-walled structures

Edge-based Smoothed Point Interpolation Method (ES-PIM) and the Node-based counterpart (NS-PIM) have been investigated as possible robust methods for dealing with highly distorted triangular-based background meshes, where the constitutive properties are assigned to nodes.

The figures above show how the background triangular-based meshes can be used to integrate the sub-domain in the edge-based approach. The left figure shows the integration cells for interior and boundary edges; the mid-figure shows how the constitutive properties are interpolated to an interior integration cell; the right figure shows the components of the normal vector of of the integration cell, which are used in the smoothed integration scheme.

These figures show how ES-PIM correlates well with FEM

Semi-analytical modelling for fast and reliable design and analysis of thin-walled structures

These models are applicable to any framework requiring fast and accurate stress analysis to obtain local field responses such as displacements, strains or stresses; or global structural responses such as modal behavior, buckling, panel flutter and so forth. Currently I work with C++, FORTRAN or Python/Cython. Common frameworks applying these models are multi-disciplinary optimization schemes, large-scale stress analysis platforms, reliability-based design and optimization, reliability-based analysis and uncertainty quantification.

In multi-fidelity frameworks, the semi-analytical models are usually coupled with data extracted from a global model to perform a local detailed analysis, allowing efficient optimization or large-scale stress analysis activities.

Multi-domain semi-analytical models

Combines the efficiency of semi-analytical models with the flexibility of multi-domain approaches, such as conventional finite elements.

These models can be applied in the modelling of stiffened panels where beam models are not sufficient to capture the applied loads, boundary conditions or expected responses. Examples are when the local buckling or local vibration of flanges and webs need to be quantified, or when post-buckled local stresses and post-buckled stiffness becomes important.

Other application cases involve local damages such as debonded regions, or when any other discontinuities are present in the analysis domain, making single-domain approaches impossible or at least very difficult to accomplish.

The following analysis models have been already developed:

  • Buckling

  • Post-buckling

  • Static analysis

  • Vibration

  • Panel flutter

  • Frequency domain fatigue for random vibration inputs (metallic structures only)

Application for stiffened panel with debonding defect

Illustration of the 15 domains interconnected for this problem

Linear buckling modes varying with the defect size and a/b ratio

Semi-analytical methods for plates, shells and stiffened panels

Development of efficient semi-analytical models for fast design of laminated composite structures. Application cases are:

  • Design/Optimization of lightweight structures

  • Linear/nonlinear analyses in panels with and without cutouts

  • Automated analysis of aircraft structures extracting internal forces and geometry from global finite element models

Illustration of the single-domain shell model for closed cylindrical and conical thin-walled structures, developed during my PhD

Predicted displacement fields for non-uniform axial loading of a cylindrical shell

Non-uniform axial loading of a conical shell

Cutout modeled with enriched semi-analytical models

Reference results from finite elements

Enriched finite elements for global models

Using the same technology applied into the development of semi-analytical models, it is possible to create enriched finite element formulations that allow a quick detailed analysis in global models.

The modified stiffness matrix assuming that no load is applied in the enriched region is described as below:

Main engineering applications are:

  • Linear/nonlinear analyses in coarse meshes with an equivalent exactness of a corresponding refined mesh

  • Addition of discontinuities like cutouts or other structural features as extra parameterized inputs (with the base mesh unchanged)