Application Of Finite Element Of B-spline Wavelet On The Interval In Structure With Cracks And Classical Laminated Plates

With complexity of engineering structures increasing, diversity of materials andthe development of computer technology, numerical calculation plays a fundamentaland important role in the design and analysis of engineering structures, it has becomeone of the essential means of modern scientific research. Because of stress singularityat the crack tip, extremely refined meshes have to be used at the crack-tip and newmeshes need to be re-divided as the crack propagates, which causes lower numericalaccuracy and efficiency for the traditional finite element method, severely influencingthe accurate identification of crack parameters. During numerical analysis ofengineering, design parameters have uncertainties due to the environmental changesand errors caused by machining and assembling. If these uncertain factors are ignored,we may get unreasonable calculation results, fuzzy mathematics is the main tool tosolve the uncertainty problem. Composite laminates are widely used in the satellitelaunch, national defense construction and other advanced technology areas because ofthe advantages of high specific strength and high specific stiffness, good corrosionresistance and material properties. However, the anisotropy of the material, layer ofstructure as well as the complexity of the edge stress distribution makes it difficult forthe traditional finite element method. Therefore, the researches on how to improve thenumerical calculation accuracy and efficiency of structures with cracks and compositelaminates plates,and combine fuzzy mathematics with numerical analysis of fracturehave become one of the focused topics. As a new numerical calculation method,BSWI employs wavelet scaling function or wavelet function of BSWI as interpolationfunction, it has a lot of good properties, such as less undetermined coefficients, highapproximation accuracy, strong localized performance and multi-resolution analysis,all of which can make up the defects for traditional finite element to solve the crackproblems and the laminated composite plates. At present, BSWI finite element methodhas been widely used in lots of fields, such as the numerical solution of partialdifferential equations, fault diagnosis, stress analysis of variable load and geometricnonlinear problems, however, the studies of numerical calculation of the fractureparameter, uncertainties analysis and stress analysis of laminated composite plates are less. In view of this, BSWI finite element method is applied to numerical calculationof the structure with cracks and laminated composite plates, a series of novelapproaches are proposed here to improve the numerical calculation accuracy andefficiency.BSWI functions have lots of good localized features, which can use fewer unitsand the number of degrees of freedom to maximize the approximation of the unknownfunction, as a result, virtual crack closure technique is proposed by applying BSWIfinite element to numerical calculation of the fracture parameter. Moreover, BSWIfinite element model with cracks is established, the node displacements at crack tip areattached by dummy node to fracture elements, stress intensity factor is calculated byvirtual crack closure technique, comparison the calculated results with those byANSYS shows that the method put forward in this paper is easy to calculate, withhigher accuracy and less elements, provides a new way for engineering fractureanalysis of structure with cracks.In order to solve the impact caused by uncertainties of loads and materials inengineering practices for numerical calculation of fracture, fuzzy finite elementmethod based on B-spline wavelet on the interval for structure with cracks is proposedby combining fuzzy theory and BSWI finite element theory with fracture mechanics.The BSWI fuzzy finite element model with cracks is established, the BSWI fuzzyequilibrium equations is deduced, specially, a strategy, Level cutting collection λ andthe interval number decomposition method are adopted to solve the intervalequilibrium equations. The analysis results demonstrate that the proposed method canaccurately reflect changes in structural response with fewer elements, moreover, thisapproach provides a new way for engineering fracture analysis with uncertaintiescomplex structures.The appearance and extension of tiny cracks in the structure may lead tocatastrophic accidents. Therefore, predicting the presence of tiny cracks andquantitative identification of parameters has important values to practical engineering.Local stiffness changes of the structure will be caused by emergence of crack,following by the modification of structural dynamics characteristics, based on this,from the view of linear elastic fracture mechanics, the identification model of crackbeam of BSWI finite element is established by using the spring element simulation ofcrack quantitative identification of cracked beam,which is finished by using crack fault diagnosis algorithm of BSWI finite element, the numerical simulation andexperimental study verify the accuracy and feasibility of the algorithm.Laminated composite plates have coupling effects of tension-shear, bending-torsion, tension with shear-bending and torsion with the complexity of the edgestress distribution, which are difficult to calculate for the traditional finite element. Tosolve this problem, BSWI finite element methods is combined with the classicallaminated plate theory in this paper, the BSWI finite element method for stressanalysis of classical laminates is proposed. Using the same scale but the differentorder BSWI scaling function tensor product interpolation constructs the element ofBSWI classical laminated plate, so BSWI finite element equilibrium equation of theclassical laminated plate is derived, the numerical simulation verifies the feasibility ofthe algorithm and accuracy.