Purpose: Materials with porosity gradient functionally gradient properties reflect changes in the material's position spatially in response to changes in porosity. One porous metal comprised the FGM core and had not previously been considered in bending analyses. Design/methodology/approach: Analytical formulations were derived based on the classical beam theory (CBT). According to the power-law scheme, the material properties of FG beams are supposed to vary along the thickness direction of the constituents. Findings: The results show that the porosity and power gradient parameters significantly influence flexural bending characteristics. It is found that there is a fair agreement between the analytical and numerical results, with a maximum error percentage not exceeding 5%. Research limitations/implications: The accuracy of analytical solutions is verified by employing the finite elements method (FEM) with commercial ANSYS 2021 R1 software. Practical implications: FGM beams' elastic properties with an even porosity distribution through-beam core and bonded with two thin solid skins at the upper and lower surfaces were carried out. Originality/value: This paper develops an analytical study to investigate the flexural problem of a functionally graded simply supported sandwich beam with porosities widely used in aircraft structures and biomedical engineering. The objective of the current work is to examine the effects of some key parameters, such as porous ratio, power-law index, and core metal type, on the flexural properties such as bending load, total deformation, and strain energy.
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A numerical analysis of the effect of temperature on the dynamics of the sandwich beam model with a viscoelastic core is presented. The beam under analysis was described with a standard rheological model. This solution allows one to study the effect of temperature on material strength properties. Calculations were performed with the Finite ElementMethod in the ANSYS software. The analysis of the results of the numerical calculations showed a significant influence of temperature on the strength properties of the model under test. The analysis confirmed damping properties of viscoelastic materials.
Purpose: In this study, the free vibration analysis of functionally graded materials (FGMs) sandwich beams having different core metals and thicknesses is considered. The variation of material through the thickness of functionally graded beams follows the power-law distribution. The displacement field is based on the classical beam theory. The wide applications of functionally graded materials (FGMs) sandwich structures in automotive, marine construction, transportation, and aerospace industries have attracted much attention, because of its excellent bending rigidity, low specific weight, and distinguished vibration characteristics. Design/methodology/approach: A mathematical formulation for a sandwich beam comprised of FG core with two layers of ceramic and metal, while the face sheets are made of homogenous material has been derived based on the Euler–Bernoulli beam theory. Findings: The main objective of this work is to obtain the natural frequencies of the FG sandwich beam considering different parameters. Research limitations/implications: The important parameters are the gradient index, slenderness ratio, core metal type, and end support conditions. The finite element analysis (FEA), combined with commercial Ansys software 2021 R1, is used to verify the accuracy of the obtained analytical solution results. Practical implications: It was found that the natural frequency parameters, the mode shapes, and the dynamic response are considerably affected by the index of volume fraction, the ratio as well as face FGM core constituents. Finally, the beam thickness was dividing into frequent numbers of layers to examine the impact of many layers' effect on the obtained results. Originality/value: It is concluded, that the increase in the number of layers prompts an increment within the frequency parameter results' accuracy for the selected models. Numerical results are compared to those obtained from the analytical solution. It is found that the dimensionless fundamental frequency decreases as the material gradient index increases, and there is a good agreement between two solutions with a maximum error percentage of no more than 5%.
Sandwich structures are certain specific type of composites, which are widely used in modern engineering. In this paper the vibration analysis of a specific type of sandwich beam is performed. The considered structure is not only non-symmetric towards its midplane, but also made of periodically varying isotropic materials. As a result, the governing equations of such complicated structure is characterised by periodic, non-continuous and highly oscillating coefficients. With the use of the tolerance averaging technique those equations are transformed into the form with constant coefficients. Eventually, a comparative simulations of free vibration analysis of several sandwich beams were conducted to verify the effectiveness and superiority of proposed calculation method over the FEM.
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Rozważa się belkę wielowarstwową wyciętą z pasma płytowego złożonego z grubych warstw ortotropowych i znajdującego się w warunkach zginania walcowego. Na powierzchni górnej belka poddana jest działaniu obciążenia dowolnie rozłożonego wzdłuż jej długości. Dolna powierzchnia jest nieobciążona. Opracowano model matematyczny, w którym rozpatrywana belka znajduje się w płaskim stanie odkształcenia. Model opisuje się układem dwóch sprzężonych równań różniczkowych sformułowanych w pochodnych cząstkowych. Rozwiązanie tego układu wybiera się w postaci sumy iloczynów nieznanych funkcji jednej zmiennej i funkcji trygonometrycznych innej zmiennej. Naprężenia i przemieszczenia w płycie wyraża się przez odpowiednie funkcje kształtu pomnożone przez nieznane parametry modelu za pomocą których spełnia się warunki powierzchniowe, brzegowe i warunki ciągłości na powierzchniach podziału warstw. Jako przykład rozważa się belkę trójwarstwową swobodnie podpartą na końcach i obciążoną siłą skupioną przyłożoną w środku rozpiętości powierzchni górnej. Otrzymane rozwiązanie z dużą dokładnością spełnia wszystkie warunki nałożone na rozpatrywany układ.
EN
Strip cut from infinite long plate compounded with thick orthotropic layers is considered in this paper. The strip is in cylindrical bending conditions and it is load by transversal loading arbitrary distributed on its upper surface while its low surface is unloaded. The mathematical model of such strip as multilayered beam working in plane strain state is worked. The model is described with two system od differential equations in particular derivatives. The solution of this system has been taken in form of products of unknown function depending on some variable and trygonometrical function depending on other one. Stresses and displacements in the plate are expressed over corresponding functions of form multiplied by unknown parameters of the model. Using these parameters the boundary conditions are performed at the outer surfaces of the strip, at its edges and in multilayered surfaces. As an example, the three layered free supported beam loaded with concentrated force applied in the center of its length is considered. The obtained solution satisfy all conditions applied on considered system with high accuracy.
The paper is devoted to the strength analysis of a simply supported three layer beam. The sandwich beam consists of: two metal facings, the metal foam core and two binding layers between the faces and the core. In consequence, the beam is a five layer beam. The main goal of the study is to elaborate a mathematical model of this beam, analytical description and a solution of the three-point bending problem. The beam is subjected to a transverse load. The nonlinear hypothesis of the deformation of the cross section of the beam is formulated. Based on the principle of the stationary potential energy the system of four equations of equilibrium is derived. Then deflections and stresses are determined. The influence of the binding layers is considered. The results of the solutions of the bending problem analysis are shown in the tables and figures. The analytical model is verified numerically using the finite element analysis, as well as experimentally.
PL
Wielowarstwowe konstrukcje są badane od wielu lat i wytwarzane z różnych materiałów, w szczególności rdzeń z materiałów porowatych, komórkowych czy tworzyw sztucznych, w tym pianek metalowych. Szczególne znaczenie w budowie maszyn lub budownictwie mają te konstrukcje, które charakteryzują się dużą wytrzymałością przy stosunkowo niewielkiej masie. Takimi konstrukcjami są właśnie struktury warstwowe, których gęstość rdzenia jest znacznie mniejsza od gęstości okładzin. Z uwagi na ich charakterystyczne własności, takie jak odporność na obciążenia dynamiczne czy absorpcja akustyczna, są szeroko stosowane chociażby w budowie satelitów, statków kosmicznych, przemyśle lotniczym, samochodowym, kolejowym i stoczniowym. Konstrukcje warstwowe wytwarzane są również współcześnie, a ich modelowanie jest nadal aktualnym tematem badań, co jest zauważalne w licznych publikacjach. Przedmiotem pracy jest analiza wytrzymałości pięciowarstwowej belki, której warstwy zewnętrzne (okładziny) połączone są z rdzeniem wykonanym z pianki aluminiowej cienkimi warstwami. Właściwości mechaniczne i fizyczne są różne dla każdej z warstw.
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The paper deals with numerical modeling of sandwich beams with polyurethane foam core and two types of face layers – short fiber reinforced composite faces and hot-zinc dipped steel sheet, coated by plastic. The experimental results of four-point bending test are used as benchmark in the commercial ANSYS program simulations.