Buckling analysis of periodic Vierendeel beams by a micro-polar homogenized model

Penta, Francesco

doi:10.1007/s00707-020-02660-4

Cited by 6 publications

(5 citation statements)

References 40 publications

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“…(50) evaluated with k = 1. Equation ( 51) has the same formal structure as the Engesser buckling load [15] and the equivalent girder Euler load derived in [51] and given by Eq. ( 42) evaluated with k = 1.…”

Section: (K)mentioning

confidence: 99%

“…The corresponding equilibrium equations, however, cannot be solved in closed form, and the finite element method reported in [50] is adopted. Some closed-form solutions for the buckling modes and critical loads of the Vierendeel girder are given in [51]. The continuous micro-polar model from which they are derived is based on the eigen-analysis of the unit cell transfer matrix [19,52,53].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, the discrete girder response to sinusoidal self-equilibrated systems of inner bending moments (self-moments) is analysed. Next, the large-deflection equilibrium problem of the micropolar model of [51] is solved.…”

Section: Introductionmentioning

confidence: 99%

“…The remainder of this paper is organized as follows. Section 2 synthetically reviews the main aspects of the micro-polar girder model of [51]. In Sect.…”

Section: Introductionmentioning

confidence: 99%

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Self-moments stiffening effect and buckling strength of periodic Vierendeel beams

Penta

2020

Acta Mech

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This paper deals with the buckling phenomenon of periodic Vierendeel beams. Closed-form solutions for critical loads and deformed shapes are presented. They are built by exploiting several auxiliary solutions obtained for the discrete periodic girder and for a geometrically nonlinear micro-polar equivalent model. In particular, the girder when subjected to sinusoidal self-equilibrated systems of inner bending moments (self-moments) is analysed. The corresponding results are used for solving the large-deflection equilibrium problem of the continuous equivalent model by means of the eigenfunction expansion technique. Girder buckling conditions are then defined in terms of kinematics of the micro-polar model: more precisely, they are attained when special distributions of self-moments, able to bend the continuous system without violating compatibility of shear strains, act in the girder. It is shown that these systems, neglected in the theories presented so far, have a significant stiffening effect on the buckling girder behaviour. Moreover, they are governed by the continuity equation for micro-rotations that is solved in closed form by the Galerkin method, with the micro-polar model eigenfunctions as basis functions. The accuracy of the proposed solutions is verified by comparing them with those achieved by a series of finite element girder models.

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Section: (K)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The remainder of this paper is organized as follows. Section 2 synthetically reviews the main aspects of the micro-polar girder model of [51]. In Sect.…”

Section: Introductionmentioning

confidence: 99%

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Self-moments stiffening effect and buckling strength of periodic Vierendeel beams

Penta

2020

Acta Mech

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“…Of these formulations, the micropolar theory has been shown to produce reliable results for sandwich structures that have structural hierarchy (e.g. [6,20,28,29,33]). However, the applications of these theories to structural design are still lacking.…”

Section: Introductionmentioning

confidence: 99%

Design space for bifurcation buckling of laser-welded web-core sandwich plates as predicted by classical and micropolar plate theories

Romanoff

Karttunen

Varsta

2020

Ann. Solid Struct. Mech.

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The strength of laser-welded web-core sandwich plates is often limited by buckling. In design of complex thin-walled structures the combination of possible structural and material combinations is basically infinite. The feasibility of these combinations can be assessed by using analytical, numerical and experimental methods. At the early design stages such as concept design stage, the role of analytical methods is significant due to their capability for parametric description and extremely low computational efforts once the solutions have been established for prevailing differential equations. Over the recent years significant advances have been made on analytical strength prediction of web-core sandwich panels. Therefore, aim of the present paper is to show impact of this development to the design space of web-core sandwich panels in buckling. The paper reviews first, briefly the differential equations of a 2-D micropolar plate theory for web-core sandwich panels and the Navier buckling solution for biaxial compression recently derived by Karttunen et al. (Int J Solids Struct 170(1):82–94, 2019) by exploiting energy methods. By comparing the micropolar and widely-used classical first-order shear deformation plate theory (FSDT) solutions, it is shown that the different equivalent single layer (ESL) formulations and plate aspect ratios have a significant impact on the practical outcomes of the feasible design space and this way motivating further developments for micropolar formulations from practical structural engineering viewpoint.

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Fundamental Theories of Aeronautics/Mechanical Structures: Past and Present Reddy’s Work, Developments, and Future Scopes

Dhimole

Cho

2022

Int. J. Aeronaut. Space Sci.

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Buckling analysis of periodic Vierendeel beams by a micro-polar homogenized model

Cited by 6 publications

References 40 publications

Self-moments stiffening effect and buckling strength of periodic Vierendeel beams

Self-moments stiffening effect and buckling strength of periodic Vierendeel beams

Design space for bifurcation buckling of laser-welded web-core sandwich plates as predicted by classical and micropolar plate theories

Fundamental Theories of Aeronautics/Mechanical Structures: Past and Present Reddy’s Work, Developments, and Future Scopes

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