143 research outputs found
Developing metamodels for fast and accurate prediction of the draping of physical surfaces
No full textIn this paper, the use of methods from the meta- or surrogate modeling literature, for building models predicting the draping of physical surfaces, is examined. An example application concerning modeling of the behavior of a variable shape mold is treated. Four different methods are considered for this problem. The proposed methods are difference methods assembled from the methods kriging and proper orthogonal decomposition (POD) together with a spline-based underlying model (UM) and a novel patchwise modeling scheme. The four models, namely kriging and POD with kriging of the coefficients in global and local variants, are compared in terms of accuracy and numerical efficiency on data sets of different sizes for the treated application. It is shown that the POD-based methods are vastly superior to models based on kriging alone, and that the use of a difference model structure is advantageous. It is demonstrated that patchwise modeling schemes, where the complete surface behavior is modeled by a collection of locally defined smaller models, can provide a good compromise between achieving good model accuracy and scalability of the models to large systems.</p
Formulation of Cohesive Finite Element for Analysing Strength of Wrinkles in Glass-Epoxy Laminates
No full textThis master thesis describes the formulation and use of Cohesive Zone Modelling in the framework of the Finite Element Method. A Cohesive Element is programmed and then validated through a number of comparisons with results from the literature. Difficulties arising when using this method are addressed, and implications hereof are discussed. Subsequently the element is used for analysing the strength of wrinkle defects in Glass-Epoxy Laminates. This is done by studying the influence of the geometrical parameters of the wrinkle through a parametric study. Through a normalised study this is used to propose a simple expression to estimate the strength reduction due to the wrinkle
Improved Damage Tolerance of Composites by Promoting Multiple Delaminations - Quasi-Static Loading
No full textMethods for Decreasing the Total Solution Time of Linear Buckling Finite Element Analyses
No full textThis master thesis is devoted to developing methods for decreasing the total solution timeof linear buckling analyses, with a large number of load combinations. Four methodsfor decreasing the total solution time is presented, along with performance studies of themethods, highlighting the methods pros and cons along with limitations.The thesis starts by giving an introduction to the method that is presently used for performinglinear buckling analyses of structures with a high amount of load combinations.The introduction includes a flowchart of the solution procedure when calculating the bucklingloads by the finite element method. After the presentation of the solution procedure,initial studies are conducted to determine the time consumption of some of the steps inthe solution procedure. These studies are conducted in order to determine which steps inthe solution procedure has the best potential for decreasing the solution time.Based on the initial studies, methods for decreasing the total solution time are proposed.The possible methods are shortly explained, to give an understanding of the main idea ineach proposed method. Next the methods for further study are selected, based on theirpotential to decrease the solution time and if it is possible to implement the method in astand alone program, or as add-on to existing commercial software. After the selection ofmethods, the geometry, used in the performance studies is presented, and the modelingof the structure is described.Theory governing the linear buckling is given. The distinction between bifurcationbuckling and limit point buckling is outlined, and the stability criterion is derived fromthe total potential energy of a system. Furthermore, the calculation of buckling loads bythe finite element method is explained. Ending the theory chapter is a presentation of thelimitations concerning the linear buckling analysis.The solution methods chosen earlier is presented, and explained further. The solutionprocedure of each method is explained in a flowchart and the theory governing the featuresused in the method is explained. The performance studies is explained and the resultsare commented and evaluated. One solution method reduces the total solution time upto 78%, according to the presently used method. Another solution method reduces thenumber of load combinations by 74%
Optimisation of Composite Structures Using Lamination Parameters in a Finite Element Application
No full textThis Master's thesis deals with mathematical optimisation of composite structures. A new method is presented, in which it is attempted to overcome the non-convex nature often associated with optimisation of composite structures modelled with finite elements. First of all, the underlying theory is presented. The brief overview of shell theory is given, and the formulations needed in order to incorporate it into a finite element analysis application are derived. That is, the geometric representations needed are established, followed by an expression for the strain-displacement matrix. From this the layer-wise thickness integration needed to obtain the stiffness for a laminate structures is studied and used to derive an expression for performing explicit thickness integration instead, which involves slight approximations of the element Jacobian. Further approximations can, however, be made resulting in an expression for doing approximate explicit thickness integration. On top of the stiffness formulations the constitutive relations are addressed. Aided by the lamina invariants, the constitutive relations are rephrased to include the lamination parameters assuming that the laminate under inspection is composed of only a single material through all layers (with different orientations though). The result of this, in combination with the formulation of explicit thickness integration, is that the element stiffness matrix is seen to be linear in the lamination parameters. The above reformulations are at last verified numerically and seen to give accurate results. Furthermore it is seen that the expression of explicit thickness integration is especially efficient when working with laminates consisting of many layers. Based on the presented theory the newly developed method is presented. First of all, the focus is brought to maximum stiffness optimisation with reference to the standard model, which is done by minimising the compliance. With the expressions of explicit thickness in hand the sensitivities needed for such an optimisation can be determined analytically, which is verified numerically to give accurate results. The method of optimisation is based on a patch-compatible parameterisation where lamination parameters play an essential role. In order to overcome the non-convex nature of the optimisation problem some characteristics of lamination parameters are studied, namely the problem of feasibility and the question of convexity of the objective function. If the objective function is optimised with lamination parameters as design variables the strain energy is in fact convex. However, this approach would give problems with ensuring feasibility of the final result. Hence the problems are sought solved by keeping the fibre orientations of the laminate as design variables and then overcoming the non-convex nature of the problem by designing the optimisation method as a two-step approach. Thus some of the ideas from the two-step approach presented by [Foldager,1999] are utilised in combination with results from [Kann and Sørensen,2010] in order to develop a new and more robust two-step method. The method developed includes an identification process where an identification function based on a local linearisation is minimised by the use of a genetic algorithm. The developed method have been implemented in MUST with the ability to switch between different numbers of applied lamination parameters in the identification process as well as both a full and an approximate method. In order to test the new method numeric experiments have been conducted. Three simple problems of "academic character" are presented - a cantilever beam with a distributed load, a flat plate with a uniform pressure normal to the surface, and a pinched hemisphere with different curvature-to-thickness ratios. The three examples show that successful identification is indeed found in several instances, meaning that a local minimum can be overcome. However, the success is dependent on a several-to-one relationship between the number of design variables and the number of lamination parameters. Furthermore the results indicate that one of the first problems arising, when doing stiffness optimisation of composite structures, seems to be that the design variables get stuck at the bounds of the design space. Asides from the experiments of "academic character", a more "industrial/practical" experiment has been conducted as well. The geometry under inspection is a generic main spar from a wind turbine blade. The conclusion from this experiment is first and foremost that the method can indeed be used on large industrial structures. Furthermore the results are close to what would be expected, however, there are small differences. These differences can be explained by the patch breakdown and effects of so small magnitude that they cannot be captured numerically. Finally, there is a strong indication that post-processing of the optimised structure is indeed necessary, as the design typically contains features which cannot be realised, or maybe is too complicated or too impractical for the manufacturer to fully realise the optimised structural design. The amount of time needed for post-processing may be reduced by incorporating restrictions associated with the manufacturing process into the numerical optimisation routines.</p
Fatigue characterization of multiple delaminations
No full textThis thesis investigates whether the overall toughness of the material can be improved by promoting multiple delaminations. This is done by first investigating state-of-the-art methods regarding materials that exhibit toughening behaviour during fracture initiation. This behaviour can be achieved by introducing weakening patches between the material interfaces. In order to validate the results found in the literature, experimental testing of a glass fiber reinforced polymer (GFRP) double cantilever beam (DCB) containing a weakening patch configuration was conducted. These DCB specimens were tested under quasi-static and fatigue loading conditions. The results showed that under quasi-static loading, no toughening was observed in the DCB beams tested. In the context of fatigue testing, the characterization of this test revealed toughening behaviour in the test specimens. These studies proposed a novel contribution to state-of-the-art methods by providing a new benchmark case for the study and prediction of multiple fatigue-driven delaminations in GFRP specimens
Inverse Parameter Identification for Multilinear Cohesive Laws
No full textThrough this report a methodologyfor characterization of fracture relatedparameters for numerical modelling ofdelamination in composite materials isdeveloped. The methodology relies onconcepts of inverse parameter identificationand optimization techniques. Thenumerical modelling is done through useof the finite element method and cohesivezone modelling.An experiment is simulated in a parametricfinite element model and a residual isdefined as the discrepancy in some givenresponse from the numerical model andthe physical experiment. The parameteridentification is then done by minimizationof the residual.The crack propagation is modelled usinguser-defined interface elements throughANSYS. A mixed mode multilinear cohesivelaw for the user-defined interface elementis developed for this purpose. Sincethe parameter identification is based on optimizationtechniques, much time is spenton formulating a proper objective function.Initially, the objective function is based onglobal structural response, but use of localmeasurements in the fracture process zoneis also investigated.The motivation for this method is to reduceusual assumptions involved in characterizationof cohesive zone parameters,increase the practical applicability by notlimiting the approach to coupon testing,and gain as much information from few butcostly experiments
Optimization Formulations for the Maximum Nonlinear Buckling Load of Composite Structures
No full textThis paper focuses on criterion functions for gradient based optimization of the buckling load of laminated composite structures considering different types of buckling behaviour. A local criterion is developed, and is, together with a range of local and global criterion functions from literature, benchmarked on a number of numerical examples of laminated composite structures for the maximization of the buckling load considering fiber angle design variables. The optimization formulations are based on either linear or geometrically nonlinear analysis and formulated as mathematical programming problems solved using gradient based techniques. The developed local criterion is formulated such it captures nonlinear effects upon loading and proves useful for both analysis purposes and as a criterion for use in nonlinear buckling optimization. © 2010 Springer-Verlag.This paper focuses on criterion functions for gradient based optimization of the buckling load of laminated composite structures considering different types of buckling behaviour. A local criterion is developed, and is, together with a range of local and global criterion functions from literature, benchmarked on a number of numerical examples of laminated composite structures for the maximization of the buckling load considering fiber angle design variables. The optimization formulations are based on either linear or geometrically nonlinear analysis and formulated as mathematical programming problems solved using gradient based techniques. The developed local criterion is formulated such it captures nonlinear effects upon loading and proves useful for both analysis purposes and as a criterion for use in nonlinear buckling optimization. © 2010 Springer-Verlag
Development of test tool for evaluation of cohesive zone parameters in DCB composite specimens
No full textDette kandidat projekt på uddannelsen Design af Mekaniske Systemer (DMS) vedAalborg Universitet, omhandler udviklingen og tilblivelsen af et testfikstur til bestemmelseaf brudmekaniske parametre i glasfiberforstærkede, såkaldte double cantileverbeam (DCB) emner. Test fiksturet, der er konstrueret på Aalborg Universitet, eri stand til at teste for brudmekaniske revne parametre under modus I såvel sommodus II og blandingsmodus mellem I og II. For at verificere testfiksturet er etværktøj fabrikeret, hvorpå strain gauges er monteret. Sammen med digital imagecorrelation (DIC) og en i et specielt fikstur indbygget last celle, har det derved væretmuligt at verificere at der under tests ikke bliver introduceret urigtige snitkræfter.Test fiksturet har været anvendt til at teste DCB emner fremstillet af glasfiber ogepoxy. Som revnestarter er der indlagt en 20 μm tynd slipfilm mellem de midterstelag i laminatet. Der er testet for modus II uden success da ingen revnevækst blevobserveret. For blandingsmodus, med modusforholdet 0.5, er der yderligere udførtforsøg. Her blev revnevækst observeret i ét forsøg. Forsøgene måtte dog afbrydespga. store rotationer af prøveemnet. Derimod er der ved modus I, på bagrundaf tests, fundet en kritisk energifrigørelsesgrad, som er anvendt i et programmeretscript til brug ved FEM analyse. Her er de ved tests fundne data anvendt til atsimulere revnevækst for lignende emner.This master thesis main goal has beento develop a test tool, to test for fracturemechanics parameters under modeI, mode II and mode mixity loading usingpure moments. The tests specimensare double cantilever beam (DCB) specimens,made from fiber reinforced composites.The test tool, that has been developedand manufactured at AalborgUniversity. For the verification, thatthe test tool produces the correct momentsand no spurious shear forces areintroduced during a test, a test devicewith strain gauges bonded, has beenused together with Digital image correlation(DIC). The test tool has beenused to test specimens fabricated fromfiberglass and epoxy. Here a 20 μm slipfilm has been inserted between the middlelayers to act as a crack starter. Successfulmode I tests were conducted andthe fracture parameters were used in aprogrammed finite element script capableof simulating the fracture process ofa specimen with the same properties asthe one tested
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