Nonlinear analysis of laminated composite plates and shells with delaminations using finite element method

Abstract

Laminated composites play an important role in the construction of aircrafts, windturbines, ships, cars and other components in mechanical and civil engineering. Forexample, the aerospace structures are made of thin-walled cylindrical or sphericalcomposite shell components having an excellent stiness-to-weight and strength-toweightratios. It is also well-known that Fiber Reinforced Polymer strengtheningof the RC beams and slabs give excellent structural results, low time required andmoderate cost. Finally, sandwich plates are widely used in civil engineering as roofand wall panels to provide the thermal isolation of the buildings. For these reasons,numerical analysis of laminated composite and sandwich structures attractthe increasing attention of researchers in the various engineering disciplines.It is very important that perfect bond between the adjacent layers within thelaminate remain intact for the panel to perform on the designed level. However,the mismatch of material properties between the adjacent layers, along with someother factors, may cause a delamination that reduces the stiness of the componentand leads to the unexpected structural behavior. To predict the response of damagedstructure, a computational model capable to describe the kinematics of thedelaminated structures is required.Several limitations of the Equivalent Single Layer (ESL) laminate theories motivatedthe researchers to derive the rened (layerwise) plate theories for the analysisof composite laminates. Therefore, the scope of this study is based on the reductionof the 3D elasticity problem to a 2D one using the Generalized Laminated Plate Theory(GLPT) of Reddy, capable to describe the delamination kinematics. The GLPTbecame the basis for the development of enriched layered nite elements, which areapplied in the numerical solution of several structural problems. In addition, layeredplate nite elements were applied in the numerical investigation of delaminatedcomposite shells using the simple transformations presented in this study.To accurately capture the buckling phenomena of the laminated composites, aswell as for investigation of the inuence of large rotations on the transient responseof delaminated composite and sandwich plates, the geometric nonlinearity is takeninto account upon the von Karman assumptions. Beside the numerical solution, theanalytical (Navier) solution for linear transient analysis of intact rectangular simplysupported composite plates is provided based on double Fourier series...

Laminatni kompoziti igraju vaznu ulogu u izradi aviona, vetrogeneratora, brodova,automobila i razlicitih elemenata u masinstvu i gradjevinarstvu. Na primer, delovikosmickih konstrukcija su izradjeni od tankozidnih cilindricnih ili sfericnih ljuski kojeimaju odlicne odnose krutost-tezina i cvrstoca-tezina. Takodje je dobro poznato daojacanje armirano-betonskih greda ili ploca uz pomoc polimera ojacanih vlaknimadaje odlicne rezultate u konstrukcijama, uz mali utrosak vremena i umereno visokucenu. Konacno, sendvic ploce se siroko primenjuju u gradjevinarstvu u vidu krovnihili fasadnih panela kako bi se obezbedila termicka izolacija zgrada. Iz ovih razloga,numericka analiza laminatnih kompozitnih i sendvic konstrukcija sve vise privlacipaznju istrazivaca u razlicitim inzenjerskim disciplinama.Veoma je vazno da idealna veza susednih slojeva u laminatu ostane neostecenakako bi se panel ponasao na projektovanom nivou. Medjutim, razlika u materijalnimosobinama susednih slojeva, uz uticaj nekih dodatnih faktora, moze da izazovedelaminaciju koja smanjuje krutost konstrukcije i dovodi do njenog neocekivanogponasanja. Da bi se predvideo odgovor ostecene konstrukcije potreban je numerickimodel koji je u stanju da opise kinematiku ploce ili ljuske sa delaminacijom.Odredjena ogranicenja teorija laminatnih ploca zasnovanih na jednom ekvivalentnomsloju (ESL) motivisala su istrazivace da razvijaju slozenije (slojevite) teorijeploca za analizu laminatnih kompozita. Iz ovog razloga, predmet ovog istrazivanjazasniva se na redukciji trodimenzionalnog problema teorije elasticnosti na dvodimenzionalniproblem primenom Redijeve Opste Laminatne Teorije Ploca (GLPT), kojaje u mogucnosti da opise kinematiku delaminacije. GLPT predstavlja osnovu zarazvijanje slozenih slojevitih konacnih elemenata koji su primenjeni u numerickomresavanju razlicitih problema. Zatim su slojeviti konacni elementi ploce primenjeniu numerickom ispitivanju laminatnih kompozitnih ljuski sa delaminacijama,primenom jednostavnih transformacija koje su prikazane u ovom istrazivanju.Kako bi se precizno ispitao problem izbocavanja laminatnih kompozita, kao iza ispitivanje uticaja velikih rotacija na dinamicki odgovor kompozitnih i sendvicploca sa delaminacijama, u obzir je uzeta geometrijska nelinearnost bazirana navon Karman-ovim pretpostavkama...