An efficient isogeometric beam formulation for analysis of 2D non-prismatic beams

Vo, Duy; Li, Xuechun; Nanakorn, Pruettha; Bui, Tinh Quoc

doi:10.1016/j.euromechsol.2021.104280

Cited by 11 publications

(8 citation statements)

References 46 publications

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“…incremental approach for analysing optimal non-prismatic functionally graded beams Hassina Ziou 1 , and Mohamed Guenfoud 2…”

Section: Simplementioning

confidence: 99%

Simple Incremental Approach for Analysing Optimal Non-Prismatic Functionally Graded Beams

Ziou¹,

Guenfoud²

2023

ACAE

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This paper presents a simple incremental approach of analysing the static behaviour of functionally graded tapered beams. This approach involves dividing the non-uniform beam into segments with uniform cross-sections, and using two separate finite element models to analyse the structural behavior of slender beams (Euler-Bernoulli model) and deep beams (Timoshenko beam theory). The material properties of the beam vary according to a power law distribution through the thickness, resulting in smooth variations in the mechanical properties. The finite element system of equations is obtained using the principle of virtual work. Detailed information on the shape functions and stiffness matrix of the beam is provided, and the numerical results are evaluated and validated using data from the literature. The comparison demonstrates that the response of the functionally graded tapered beams is accurately assessed by the proposed approach. Additionally, the effects of material distribution, boundary conditions, and tapering parameter on the deflection behavior are presented. Results show that an increase in the power law index increases the flexibility of the functionally graded tapered beams, resulting in higher deflection. Furthermore, lower tapering parameters also result in higher deflection. Compared to other boundary conditions, clamped-clamped boundary conditions demonstrate the best performance in terms of maximum deflection.

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“…incremental approach for analysing optimal non-prismatic functionally graded beams Hassina Ziou 1 , and Mohamed Guenfoud 2…”

Section: Simplementioning

confidence: 99%

Simple Incremental Approach for Analysing Optimal Non-Prismatic Functionally Graded Beams

Ziou¹,

Guenfoud²

2023

ACAE

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“… 2007 ; Vo et al. 2021 ). Nevertheless, predicting tapered beam behavior through 1D beam formulations poses some challenges.…”

Section: Introductionmentioning

confidence: 99%

“…To manufacture tapered beams, modern technologies such as 3D printing and automated welding can shape beam-like structures of complex geometry. As a result, more cost-efficient structural elements can be produced by optimizing stiffness distributions (Timoshenko and Young 1945;Bai et al 2018;Vo et al 2021) while meeting design criteria. Regarding the manufacture of tapered composite laminates, two methods are employed: ply drop-off and variable prepreg tape spreading.…”

Section: Introductionmentioning

confidence: 99%

“…In addition to being lighter, non-prismatic beams can be manufactured to meet specific geometrical shapes driven by design requirements. Well-known examples include bridges, helicopter and wind turbine blades and aircraft wings (Hodges 1990;Balduzzi et al 2017d;Vinod et al 2007;Vo et al 2021). Nevertheless, predicting tapered beam behavior through 1D beam formulations poses some challenges.…”

Section: Introductionmentioning

confidence: 99%

“… 2018 ; Vo et al. 2021 ) while meeting design criteria. Regarding the manufacture of tapered composite laminates, two methods are employed: ply drop-off and variable pre-preg tape spreading.…”

Section: Introductionmentioning

confidence: 99%

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Stress recovery of laminated non-prismatic beams under layerwise traction and body forces

Vilar

Hadjiloizi

Masjedi

2022

Int J Mech Mater Des

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Emerging manufacturing technologies, including 3D printing and additive layer manufacturing, offer scope for making slender heterogeneous structures with complex geometry. Modern applications include tapered sandwich beams employed in the aeronautical industry, wind turbine blades and concrete beams used in construction. It is noteworthy that state-of-the-art closed form solutions for stresses are often excessively simple to be representative of real laminated tapered beams. For example, centroidal variation with respect to the neutral axis is neglected, and the transverse direct stress component is disregarded. Also, non-classical terms arise due to interactions between stiffness and external load distributions. Another drawback is that the external load is assumed to react uniformly through the cross-section in classical beam formulations, which is an inaccurate assumption for slender structures loaded on only a sub-section of the entire cross-section. To address these limitations, a simple and efficient yet accurate analytical stress recovery method is presented for laminated non-prismatic beams with arbitrary cross-sectional shapes under layerwise body forces and traction loads. Moreover, closed-form solutions are deduced for rectangular cross-sections. The proposed method invokes Cauchy stress equilibrium followed by implementing appropriate interfacial boundary conditions. The main novelties comprise the 2D transverse stress field recovery considering centroidal variation with respect to the neutral axis, application of layerwise external loads, and consideration of effects where stiffness and external load distributions differ. A state of plane stress under small linear-elastic strains is assumed, for cases where beam thickness taper is restricted to $$15^{\circ }$$ 15 ∘ . The model is validated by comparison with finite element analysis and relevant analytical formulations.

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Isogeometric gradient‐free proportional topology optimization (IGA‐PTO) for compliance problem

Nguyen

Bui

et al. 2023

Numerical Meth Engineering

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This study presents the incorporation of the effective gradient‐free proportional topology optimization algorithm into the framework of isogeometric analysis. The minimization of the compliance is considered, and the solid isotropic material with penalization method is used. The geometry, displacements, and density are all described by non‐uniform rational B‐spline (NURBS) basis functions. The density at an integration point is determined proportionally to its compliance. Then, the NURBS description of the density is constructed elementwise by deriving a relation between densities assigned to integration points and control points. The global NURBS description of the density for the whole domain is a blend of those from elements. Furthermore, a multiresolution scheme is presented by means of ‐refinement technique to enable the efficient performance for large‐scale problems. The accuracy and efficiency of the proposed approach are assessed through six numerical examples, including two‐ and three‐dimensional structures, with several rigorous tests and comparisons with the gradient‐based optimality criteria algorithm.

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An efficient isogeometric beam formulation for analysis of 2D non-prismatic beams

Cited by 11 publications

References 46 publications

Simple Incremental Approach for Analysing Optimal Non-Prismatic Functionally Graded Beams

Simple Incremental Approach for Analysing Optimal Non-Prismatic Functionally Graded Beams

Stress recovery of laminated non-prismatic beams under layerwise traction and body forces

Isogeometric gradient‐free proportional topology optimization (IGA‐PTO) for compliance problem

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