To cite this version:Alexandre Loredo, Alexis Castel. A multilayer anisotropic plate model with warping functions for the study of vibrations reformulated from Woodcock's work. Journal of Sound and Vibration, Elsevier, 2013, 332 (1) AbstractIn this paper, a suitable model for static and dynamic analysis of inhomogeneous anisotropic multilayered plates is described. This model takes into account the variations of the transverse shear strains through the thickness of the plate by means of warping functions. Warping functions are determined by enforcing kinematic and static assumptions at the interfaces. This model leads to: a 10 × 10 stiffness matrix coupling to each other the membrane strains, the bending and torsion curvatures, and the x and y-derivatives of the transverse shear strains; and a classical 2 × 2 transverse shear stiffness matrix. This model has been proven to be very efficient, especially when high ratios between the stiffnesses of layers -up to 10 6 -are present. This work is related to Woodcock's model, so it can be seen as a reformulation of his work. However, it brings several enhancements: the displacement field is made explicit; it is reformulated with commonly used plate notations; laminate equations of motion are fully detailed; the place of this model among other plate models is now easy to see and is discussed; the link between this formulation and the original one is completely written with all necessary proofs; misses and errors have been found in the energy coefficients of the original work and have been corrected; it is now easy to improve or to adapt the model for specific applications with the choice of refined or specific warping functions.Static deflection and natural frequencies for isotropic and anisotropic sandwich plates are given and compared to other models: they show that the present model is very accurate for the simulation of such structures.

A multilayered plate theory which uses transverse shear warping functions is presented. Two methods to obtain the transverse shear warping functions from three-dimensional elasticity equations are proposed. The warping functions are issued from the variations of transverse shear stresses computed at specific points of a simply supported plate. The first method considers an exact 3D solution of the problem. The second method uses the solution provided by the model itself: the transverse shear stresses are computed integrating equilibrium equations. Hence, an iterative process is applied, the model is updated with the new warping functions, and so on. Once the sets of warping functions are obtained, the stiffness and mass matrices of the models are computed. These two models are compared to other models and to analytical solutions for the bending of simply supported plates. Four different laminates and a sandwich plate are considered. Their length-to-thickness ratios vary from 2 to 100. An additional analytical solution that simulates the behavior of laminates under the plane stress hypothesis -shared by all the considered models -is computed. Both presented models give results very close to this exact solution, for all laminates and all length-to-thickness ratios.

No abstract

Aerospace industry OEMs and suppliers are progressing their engineering processes and performance to the next maturity level gearing to digital thread solutions. Current challenges like continuous engineering, virtual certification, distributed development, consolidated virtual proving grounds, homologation, digital twin and operational applications, require well informed decision making in a comprehensive, reliable, traceable and customizable environment. In particular, in aerospace domain, with widespread tight collaborative ecosystems between integrators and suppliers, the capability of tracing each decision and its underlying artifacts becomes a key value of an engineering platform. This paper will outline a middleware approach to reuse generated artifacts and their relationships in a federated engineering environment supporting a "best tool for the job" approach by introducing a layer providing unification and consistency throughout all managed artifacts. Based on an exemplary eVTOL setup, the benefits of integrated data and workflows from specification to virtual design verification are highlighted to motivate their value towards realisation of MBSE methodologies.

Acoustic requirements for space habitats are stringent and involve a combination of noise sources minimization and public address and general alarm (PAGA) system validation. Simulation solutions are essential for demonstrating compliance requirement as early as possible and continuously throughout the development cycle of the spacecraft. Space habitats' sound field can be computationally challenging to predict in a deterministic manner for most of the audible spectrum as the volume can be important. For this application, an initial PAGA system design assessment was performed using Ray-Tracing, a geometric statistical method, which must be validated using a deterministic method. For validation purpose, the Boundary Element Method (BEM) was chosen for this application. Given the size of the structure and the desired frequency range, the BEM model was very large, containing over 250,000 wetted nodes, and a standard BEM solver required approximately 200GB of RAM. To limit computing hardware constraints, a newly implemented commercially available H-Matrix BEM solver was used. Pressure maps of a PAGA system simulation on a generic space habitat resulting from the Ray-Tracing and H-Matrix BEM solvers are compared to a standard BEM simulation. Results are compared both in terms of accuracy and computational performance, showing the advantages of using multiple simulation methods at various stages of the design.