A homogenization method for geometric nonlinear analysis of sandwich structures with initial imperfections

Goncalves, Bruno Reinaldo; Jelovica, Jasmin; Romanoff, Jani

doi:10.1016/j.ijsolstr.2016.02.009

Cited by 29 publications

(14 citation statements)

References 22 publications

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“…With suitable extensions, the plate element will enable further study of web-core plate buckling problems. Finally, as shown by Reinaldo Goncalves et al [35] by classical ESL-FSDT and 3-D FEA, in case of geometrical non-linearity it is possible that the microstructure buckles locally instead of global buckling which was discussed in this paper. This calls for two-scale geometrical non-linear solution.…”

Section: Discussionmentioning

confidence: 60%

“…In this context, the early works to be mentioned are those of First order shear deformation theory (FSDT) as formulated by Holmberg [12] for web-core panels Libove and Batdorf [25], Libove and Hubka [26] for corrugated core panels. Since that time several formulations have been presented for analytical solutions, finite element solutions and their numerical and experimental validations, see Lok et al [27], Nordstrand [30,31], in laser-welded web-core panels by Jelovica et al [16,18,19] Jelovica and Romanoff [17] and further to cases where local buckling interacts with global buckling, see for example Patel et al [32] and interacting local and global buckling by Reinaldo Goncalves et al [35]. All these investigations show that at the conceptual level of structural design, linear bifurcation (eigenvalue) buckling forms the first estimate for the limit state function.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 60%

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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“…As the local and global deformations interact, there is a need for coupled models where the geometrical nonlinearity in one length-scale can be mapped correctly to the another one. Such example in context of classical continuum mechanics has been presented in Reinaldo Goncalves et al [46] with one way coupling and in for example Geers et al [21] and Rabzcuk et al [30] for two-way coupling. However, this work should be extended to the non-classical continuum mechanics due to the reasons mentioned above.…”

Section: Discussionmentioning

confidence: 97%

Post-buckling of web-core sandwich plates based on classical continuum mechanics: success and needs for non-classical formulations

et al. 2020

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The paper investigates the post-buckling response of web-core sandwich plates through classical continuum mechanics assumptions. The compressive loading is assumed to be in the direction of the web plates. Equivalent Single Layer (ESL) plate formulation is used with the kinematics of the First order Shear Deformation Theory (FSDT). During the initial, membrane-dominated loading stages, it is observed that the effect of finite size of the periodic microstructure is barely influences the plate responses. At the higher loads, when bending is activated, the finite size of the microstructure activates secondary shear-induced bending moments at the unit cells of the plate. A method to capture the envelope of the maximum values of these bending moments is presented. The findings are validated with the shell element models of the actual 3D-geometry. Finally, the physical limits of the classical continuum mechanics are discussed in the present context.

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“…However, the beam model as a homogenized model describing the mid-line of the beam does not describe such behavior as local bending or buckling of single lattice struts in the vicinity of concentrated loads or constrained boundaries. A homogenization method considering initial imperfections for geometrically nonlinear analysis [Reinaldo Goncalves et al 2016] could be considered to treat this issue in future studies.…”

Section: Discussionmentioning

confidence: 99%

A geometrically nonlinear Euler–Bernoulli beam model within strain gradient elasticity with isogeometric analysis and lattice structure applications

Tran

Niiranen

2020

Math. Mech. Compl. Sys.

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A homogenization method for geometric nonlinear analysis of sandwich structures with initial imperfections

Cited by 29 publications

References 22 publications

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

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

Post-buckling of web-core sandwich plates based on classical continuum mechanics: success and needs for non-classical formulations

A geometrically nonlinear Euler–Bernoulli beam model within strain gradient elasticity with isogeometric analysis and lattice structure applications

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