Analytical plane-stress recovery of non-prismatic beams under partial cross-sectional loads and surface forces

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

doi:10.1016/j.engstruct.2021.113169

Cited by 6 publications

(3 citation statements)

References 41 publications

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“…Previous research, as gleaned from these studies, predominantly targeted common structural elements such as beams [ 2 , [20] , [21] , [22] , [23] ], columns [ 6 , 12 , [24] , [25] , [26] ], bridges [ 10 , [27] , [28] , [29] ], slabs [ 21 , [30] , [31] , [32] ], and nuclear containment structures [ [33] , [34] , [35] , [36] , [37] ]. Notably, there were limited investigations into the application of tendons in special structural components like walls [ 38 ], towers [ 39 ], tunnels [ 40 ], and frames [ 41 ].…”

Section: Introductionmentioning

confidence: 99%

Performances and properties of steel and composite prestressed tendons – A review

Rafieizonooz,

Jang,

Kim

et al. 2024

Heliyon

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Section: Introductionmentioning

confidence: 99%

Performances and properties of steel and composite prestressed tendons – A review

Rafieizonooz,

Jang,

Kim

et al. 2024

Heliyon

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“…This hypothesis, however, is not appropriate to cases where the external load is applied to a portion of the cross-sectional area. Practical examples include aircraft wings, wind turbine and helicopter rotor blades under fluid pressure and shear forces; arched beams in bridges under vehicular traction forces and tensile stresses in tendons of prestressed concrete (Vilar et al 2021b). As such, an accurate and effective analytical method for stresses is necessary to exploit the full potential of laminated non-prismatic beams.…”

Section: Introductionmentioning

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%

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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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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Analytical plane-stress recovery of non-prismatic beams under partial cross-sectional loads and surface forces

Cited by 6 publications

References 41 publications

Performances and properties of steel and composite prestressed tendons – A review

Performances and properties of steel and composite prestressed tendons – A review

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

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

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