Stress analysis of generally asymmetric non-prismatic beams subject to arbitrary loads

Vilar, M.M.S.; Hadjiloizi, D.A.; Masjedi, Pedram Khaneh

doi:10.1016/j.euromechsol.2021.104284

Cited by 14 publications

(8 citation statements)

References 41 publications

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“…The adopted geometrical description implies that cross-sections are non-orthogonal to the beam's neutral axis. Instead, orthogonality is preserved in the Cartesian coordinate system, noting similar methodology is adopted in related works (Balduzzi et al 2016;Gimena et al 2008;Rajagopal and Hodges 2014;Balduzzi et al 2017a, c, d;Mercuri et al 2020;Vilar et al 2021a). Consequently, the cross-sectional layer area A (k) and total cross-sectional area A are given by The domain of each layer Ω (k) is then defined by…”

Section: Problem Idealizationmentioning

confidence: 99%

“…For single layered beams, Eq. (2.10) simplifies to the equilibrium equations of homogeneous tapered beams (Vilar et al 2021a;Balduzzi et al 2016Balduzzi et al , 2017c.…”

Section: Equilibrium Relationsmentioning

confidence: 99%

“…Noting that the taper angle is limited to 15 • to reduce error of Eq. (3.1) (Boley 1963;Balduzzi et al 2016;Vilar et al 2021a).…”

Section: Stress Field Recoverymentioning

confidence: 99%

“…Chockalingam et al (2020) derived the shear stress of I-beams tapered in the thickness and width directions. Also, Vilar et al (2021aVilar et al ( , 2021b recovered the 2D stress field of non-prismatic beams subject to generalized and partial cross-sectional loads, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…In general, classical beam models generalize the external load through the entire crosssection. This hypothesis, although not best representing surface forces and partial cross-sectional loads, is widely accepted in beam modeling approaches (Masjedi et al 2019;Weaver 2020a, b, 2022;Masjedi et al 2021;Doeva et al 2020aDoeva et al , b, 2021Doeva et al , 2022Balduzzi et al 2019;Bertolini et al 2019;Bertolini and Taglialegne 2020;Chockalingam et al 2020Chockalingam et al , 2021Vilar et al 2021a). Another issue not addressed in analytical laminated beam formulations is for cases where the stiffness distribution is different from the transverse and axial load distributions, which gives rise to non-classical transverse stresses.…”

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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Section: Problem Idealizationmentioning

confidence: 99%

“…For single layered beams, Eq. (2.10) simplifies to the equilibrium equations of homogeneous tapered beams (Vilar et al 2021a;Balduzzi et al 2016Balduzzi et al , 2017c.…”

Section: Equilibrium Relationsmentioning

confidence: 99%

“…Noting that the taper angle is limited to 15 • to reduce error of Eq. (3.1) (Boley 1963;Balduzzi et al 2016;Vilar et al 2021a).…”

Section: Stress Field Recoverymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Exact Analytical Solution of the Pure Bending Problem of a Multilayer Wedge-Shaped Console

Ковальчук

Goryk

Antonets

2022

Lecture Notes in Mechanical Engineering

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3D Numerical Cross-Section Analysis of a Tapered Beam Slice

Sarhadi,

Eder

2024

Iran J Sci Technol Trans Mech Eng

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Cross-section analysis is an important tool used to recover stresses and strains in a structure at specific cross-sections of arbitrary geometries, without the need for a full 3D model. This is particularly essential for large-scale structures such as aircrafts, wind turbine blades, etc. where making a full model can be computationally very expensive or impractical. The majority of currently available cross-section analysis frameworks are based on stepwise prismatic assumptions, which are hardly suited for the analysis of tapered beams. In fact, high-fidelity stress analysis obtained from analytical and full 3D models shows that predictions of stepwise prismatic approximations can significantly deviate from the correct solution of tapered beams. In this work, a prismatic 3D cross-section analysis method is extended to analyze a symmetrically tapered finite cross-section slice. In this study, the cross-section slice is discretized with 8-node and 20-node solid elements. The boundary conditions are applied as six constraint equations via the Lagrange multiplier method. The external nodal forces acting on the cross-section faces are obtained from the equivalent tractions induced by the cross-section forces. The developed numerical model is validated against the exact analytical solutions of a wedge as well as commercial finite element (FE) software COMSOL and it is shown that the numerically predicted displacement and stress fields agree well with those provided by the wedge’s analytical solution and the FE COMSOL results. This work contributes to the advancement of high-fidelity numerical tapered cross-section analysis methods with an application for many engineering structures.

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Stress analysis of generally asymmetric non-prismatic beams subject to arbitrary loads

Cited by 14 publications

References 41 publications

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

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

Exact Analytical Solution of the Pure Bending Problem of a Multilayer Wedge-Shaped Console

3D Numerical Cross-Section Analysis of a Tapered Beam Slice

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