Structural analysis of non-prismatic beams: Critical issues, accurate stress recovery, and analytical definition of the Finite Element (FE) stiffness matrix

Mercuri, Valentina; Balduzzi, Giuseppe; Asprone, Domenico; Auricchio, Ferdinando

doi:10.1016/j.engstruct.2020.110252

Cited by 40 publications

(19 citation statements)

References 54 publications

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“…When deriving nonlinear equations by taking into account inelastic deformation, the results obtained in [44,45] can be used. The models proposed in [25,26] could be used for improving the original model, accounting more exactly for the coupling between tangential and bending loads.…”

Section: Discussionmentioning

confidence: 99%

“…where a(ξ) = r A 2 . Using Equations ( 21) and ( 22), one obtains w 0 = w 0 (ϕ); u 0 = u 0 (ϕ) (26) Then Equation ( 23) can be rewritten as follows…”

Section: Asymptotic Homogenization Methodsmentioning

confidence: 99%

“…This method has been used in the analysis of corrugated shells since the 1930s [17]. The main disadvantage of this approach is the difficulty in estimating accuracy and the area of applicability [18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

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Buckling of Corrugated Ring under Uniform External Pressure

Andrianov¹,

Diskovsky²,

Ryzhkov³

2020

Symmetry

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Stability analysis of a corrugated ring subjected to uniform external pressure is under consideration. Two main approaches to solving this problem are analyzed. The equivalent bending stiffness approach is often used in engineering practice. It is based on some plausible assumptions about the behavior of a structure. Its advantage is the simplicity of the obtained relations; the disadvantage is the difficulty in estimating the area of applicability. In this paper, we developed an asymptotic homogenization method for calculating the critical pressure for a corrugated ring, which made it possible to mathematically substantiate and refine the equivalent bending stiffness approach. To evaluate the results obtained using the equivalent stiffness approach and asymptotic homogenization method, the imperfection method is used. The influence of the corrugation parameters on buckling pressure is analyzed.

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Section: Discussionmentioning

confidence: 99%

“…where a(ξ) = r A 2 . Using Equations ( 21) and ( 22), one obtains w 0 = w 0 (ϕ); u 0 = u 0 (ϕ) (26) Then Equation ( 23) can be rewritten as follows…”

Section: Asymptotic Homogenization Methodsmentioning

confidence: 99%

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Buckling of Corrugated Ring under Uniform External Pressure

Andrianov¹,

Diskovsky²,

Ryzhkov³

2020

Symmetry

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“…On the macro side, it is necessary to start with the relationship between node displacement and node stiffness, and to introduce two mathematical expressions of the matrix and vector. Respectively denote the vector composed of all nodal displacements as P, the vector composed of nodal loads as R, and the structural stiffness matrix as K, then the following relation is established (Mercuri et al, 2020)…”

Section: Static Simulation Of the Battery Packmentioning

confidence: 99%

Simulation and optimization of a new energy vehicle power battery pack structure

Ruan¹,

Yu²,

Hu³

et al. 2021

Journal of Theoretical and Applied Mechanics

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With the rapid growth in new energy vehicle industry, more and more new energy vehicle battery packs catch fire or even explode due to the internal short circuit. Comparing with traditional vehicles, the new energy vehicles industry should pay more attention to safety of power battery pack structures. The battery pack is an important barrier to protect the internal batteries. A battery pack structure model is imported into ANSYS for structural optimization under sharp acceleration, sharp turn and sharp deceleration turn conditions on the bumpy road. Based on the simulation, the battery pack structure is improved, and suitable materials are determined. Then the collision resistance of the optimized battery pack is verified, and the safety level is greatly improved. While ensuring the safety and reliability of the battery pack structure, it also reduces the weight to satisfy the lightweight design and complies with relevant technical standards.

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“…Nevertheless, predicting tapered beam behavior through 1D beam formulations poses some challenges. For example, the state of stress on beam surfaces is governed by Cauchy's traction-stress relation, resulting in non-vanishing transverse stresses (Balduzzi et al 2016(Balduzzi et al , 2017a(Balduzzi et al , b, c, d, 2019Mercuri et al 2020;Hodges et al 2008Hodges et al , 2011Vilar et al 2021a, b). For heterogeneous media, Cauchy's traction-stress equation must also be satisfied on interface surfaces, which causes transverse stress discontinuities (Balduzzi et al 2017a).…”

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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Structural analysis of non-prismatic beams: Critical issues, accurate stress recovery, and analytical definition of the Finite Element (FE) stiffness matrix

Cited by 40 publications

References 54 publications

Buckling of Corrugated Ring under Uniform External Pressure

Buckling of Corrugated Ring under Uniform External Pressure

Simulation and optimization of a new energy vehicle power battery pack structure

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

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