Equivalent-Single-Layer discontinuous Galerkin methods for static analysis of multilayered shells

Guarino, Giuliano; Milazzo, Alberto; Gulizzi, Vincenzo

doi:10.1016/j.apm.2021.05.024

Cited by 14 publications

(17 citation statements)

References 65 publications

(96 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Both the static and the buckling problems are solved via the Interior Penalty DG formulation previously introduced for the static behavior of composite structures, see Refs. [40][41][42][43]. In particular, we verify that, by introducing the domain terms accounting for the initial stress distribution and retaining the same boundary integrals employed in the static analyses to enforce the inter-element continuity and the boundary conditions, the present DG formulation provides a high-order accurate solution of the buckling problem for laminated plates and shells.…”

Section: Introductionmentioning

confidence: 59%

“…( 5). Then, following Guarino et al [41,42], we assume the following through-the-thickness expansion for the covariant component…”

Section: B the Equivalent-single-layer Theory For Shellsmentioning

confidence: 99%

“…For example, the vector 𝒎 ⟨ℓ ⟩ 1 may be defined with respect to a unit vector in the global Cartesian reference system; this strategy has been tested in Ref. [41] and allows the modelling of multilayered plates where the layers are characterized by parallel straight fibers but the vectors of the curvilinear basis change as functions of 𝜉 1 and 𝜉 2 . Other choices of the layers' local reference systems may also be employed, such that those stemming from the intersection of the shell surface with a given plane, see e.g.…”

Section: Constitutive Behaviormentioning

confidence: 99%

“…However, for the sake of conciseness, the strong form of governing equations is not reported here and may be found in Refs. [40][41][42][43].…”

Section: E Static Problemmentioning

confidence: 99%

“…The DG method has been successfully employed for the static analysis of plates and shell structures modelled via the CLT [35][36][37] and the FSDT [38,39]. More recently, it has also been used to solve the governing equations of static elasticity and piezoelectricity associated with ESL [40][41][42] and LW [43][44][45] theories for multilayered plates and shells.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Accurate Multilayered Shell Buckling Analysis via the Implicit-Mesh Discontinuous Galerkin Method

2022

Self Cite

View full text Add to dashboard Cite

A novel formulation for the linear buckling analysis of multilayered shells is presented. High-order equivalent-single-layer shell theories based on the through-the-thickness expansion of the covariant components of the displacement field are employed. The novelty of the formulation regards the governing equations solution via implicit-mesh discontinuous Galerkin method. It is a high-order accurate numerical technique based on a discontinuous representation of the solution among the mesh elements and on the use of suitably defined boundary integrals to enforce the continuity of the solution at the inter-element interfaces as well as the boundary conditions. Owing to its discontinuous nature, it can be naturally employed with nonconventional meshes. In this work, it is combined with the implicitly defined mesh technique, whereby the mesh of the shell modeling domain is constructed by intersecting an easy-to-generate background grid and a level set function implicitly representing the cutouts. Several numerical examples are considered for the buckling loads of plates and shells modeled by different theories and characterized by various materials, geometry, boundary conditions, and cutouts. The obtained results are compared with literature and finite-element solutions, and they demonstrate the accuracy and the robustness of the proposed approach.

show abstract

Section: Introductionmentioning

confidence: 59%

“…( 5). Then, following Guarino et al [41,42], we assume the following through-the-thickness expansion for the covariant component…”

Section: B the Equivalent-single-layer Theory For Shellsmentioning

confidence: 99%

Section: Constitutive Behaviormentioning

confidence: 99%

“…However, for the sake of conciseness, the strong form of governing equations is not reported here and may be found in Refs. [40][41][42][43].…”

Section: E Static Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Accurate Multilayered Shell Buckling Analysis via the Implicit-Mesh Discontinuous Galerkin Method

2022

Self Cite

View full text Add to dashboard Cite

show abstract

High-order Accurate Beam Models Based on Discontinuous Galerkin Methods

Gulizzi,

Benedetti,

Milazzo

2023

Aerotec. Missili Spaz.

View full text Add to dashboard Cite

A novel high-order accurate approach to the analysis of beam structures with bulk and thin-walled cross-sections is presented. The approach is based on the use of a variable-order polynomial expansion of the displacement field throughout both the beam cross-section and the length of the beam elements. The corresponding weak formulation is derived using the symmetric Interior Penalty discontinuous Galerkin method, whereby the continuity of the solution at the interface between contiguous elements as well as the application of the boundary conditions is weakly enforced by suitably defined boundary terms. The accuracy and the flexibility of the proposed approach are assessed by modeling slender and short beams with standard square cross-sections and airfoil-shaped thin-walled cross-sections subjected to bending, torsional and aerodynamic loads. The comparison between the obtained numerical results and those available in the literature or computed using a standard finite-element method shows that the present method allows recovering three-dimensional distributions of displacement and stress fields using a significantly reduced number of degrees of freedom.

show abstract