Non-linear multi-mode buckling of non-symmetric FML/FGM thin-walled columns with open cross-sections under compression

The interactive buckling phenomenon in thin-walled channel section beams is investigated in this paper. This study deals with medium length beams made of the step-variable functionally graded materials (FGM) which consists of aluminum and titanium layers. The interaction of local, primary and secondary global buckling mode and their effect on the load-carrying capacity is discussed. The parametric studies are performed to assess the effect of the thickness of the beam’s component, its length and position of the individual layer on the equilibrium paths. Additionally, the influence of the adhesive layer between materials was analyzed. The problem was solved using the Finite Element Method.

Section: Introductionmentioning

confidence: 97%

“…Kolakowski and Mania [34] analyzed the coupling matrix B effect on the interactive instabilities in FML-FGM (Fiber Metal Laminate-Functionally Graded Material) columns. The interactive buckling in FGM-FML structures was also studied in [35].…”

Section: Introductionmentioning

confidence: 99%

Multi-Mode Buckling Analysis of FGM Channel Section Beams

Zaczynska

Kaźmierczyk

2020

“…A strong formulation finite element method for the statics and dynamics of laminated plates was proposed in [47]. The semi-analytical methods based on the classical laminate plate theory were formulated and used to consider some mechanical problems, e.g., for the dynamics and stability of functionally graded thin plates in [48]; for buckling of FML-FGM columns, made of such plates, with open cross-sections in [49]; similar columns with closed cross-sections in [50]; or for the imperfection sensitivity of the post-buckling of FML columns in [51]. Using the modified couple stress theory, a new plate model of the thermal buckling of functionally graded annular plates with microstructure was proposed in [52].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Functionally Graded Laminated (FGL) Media—Theoretical Tolerance Modelling

Jędrysiak

2023

Dynamic problems of elastic non-periodically laminated solids are considered in this paper. It is assumed that these laminates have a functionally graded structure on the macrolevel along the x1-axis and non-periodic structure on the microlevel. However, along the other two directions, i.e., x2 and x3, their properties are constant. The effects of the size of a microstructure (the microstructure effect) on the behaviour of the composites can play a significant role. This effect can be described using the tolerance modelling method. This method allows us to derive model equations with slowly varying coefficients. Some of these terms can depend on the size of the microstructure. These governing equations of the tolerance model make it possible to determine formulas describing not only fundamental lower-order vibrations related to the macrostructure of these composite solids, but also higher-order vibrations related to the microstructure. Here, the application of the tolerance modelling procedure is shown to lead to equations of the tolerance model that can be used for non-periodically laminated solids. Then, these model equations are mainly used to analyse a simple example of vibrations for functionally graded composites with non-periodically laminated microstructure (FGL). Similar problems were investigated in the framework of the homogenised (macrostructural) model (Jędrysiak et al. 2006); the resulting equations neglect the microstructure effect.

“…Reference [ 46 ], or of columns with open/closed cross-sections made of those plates, cf. Reference [ 47 , 48 ]. Free vibrations of thermally loaded functionally graded sandwich plates were investigated using three-dimensional finite element modelling in Reference [ 49 ].…”

Section: Introductionmentioning

confidence: 99%

Theoretical Analysis of Buckling for Functionally Graded Thin Plates with Microstructure Resting on an Elastic Foundation

Jędrysiak

Kaźmierczak-Sobińska

2020

In this paper, the problem of the stability of functionally graded thin plates with a microstructure is presented. To analyse this problem and take into consideration the effect of microstructure, tolerance modelling is used. The tolerance averaging technique allows us to replace the equation with non-continuous, tolerance-periodic, highly oscillating coefficients of the system of differential equations with slowly-varying coefficients, which describes also the effect of the microstructure. As an example, the buckling of a microstructured functionally graded plate band on a foundation is investigated. To obtain results, the tolerance model and the asymptotic model combined together with the Ritz method are used. It is shown that the tolerance model allows us to take into account the effect of microstructure on critical forces.