NURBS-IGA-based modelling: analysis and optimization of laminated plates

Analiza laminatnih kompozitnih ploča izloženih poprečnom opterećenju razmatra se primjenom nove metode izogeometrijske analize (IGA). Non-Uniform Rational B-Splines (NURBS) koriste se kao funkcije oblika za modeliranje geometrije konstrukcije te također kao funkcije oblika u postupku analize. Granični uvjeti su zadani primjenom jedne vrste metode kolokacija. Izvrsnost se nove metode pokazuje na nekoliko primjera koji se uspoređuju s "Galerkin element free" metodom i teoretskom metodom na kraju. Dobiveni rezultati pokazuju učinkovitost nove metode. Postupak optimalizacije proveden je primjenom metode genetičkog algoritma.Analysis of the laminated composite plates under transverse loading is considered using the new method of Isogeometric Analysis (IGA). Non-Uniform Rational B-Splines (NURBS) are used as shape functions for modelling the geometry of the structure and are also used as shape functions in the analysis process. Boundary conditions are imposed using a kind of collocation method. To show robustness of the new technique, some examples are represented and are compared with the element free Galerkin and theoretical method at the end. The obtained results show the efficiency of the method. The optimization process is done using genetic algorithm method

structural analysis of transversally loaded quasi isotropic rectilinear orthotropic composite circular plates with galerkin method

Abstract Bending analysis of rectilinear orthotropic composite plates have been scarcely investigated taking into account the increasing use of composite materials in structural applications in the last years. This kind of plates are laminates with axisymmetric geometry and they are made up of unidirectionally reinforced layers with different orientations. Transversally loading this kind of circular plates, the deflected mid-surface is not independent from the circumferential coordinate, unlike the case of isotropic circular plate. Nevertheless, the quasi-isotropic stacking sequence makes still possible to introduce the hypothesis of axisymmetry for the mid-surface deflection under transversal load, disregarding the circumferential variation of the vertical displacement connected to the variable bending stiffness. Then, the constitutive equations for this specific family of plates were obtained finding the stress resultants-strains relations in the global cylindrical coordinate system. These expressions, along with the equilibrium equations, made it possible to derive the governing equation of the problem in the frame of Kirchhoff-Love hypothesis of the classical lamination theory. The Galerkin method was applied to solve the governing third order differential equation in terms of mid-surface deflection, introducing appropriate polynomial approximation functions compliant with the boundary conditions. In particular, fully clamped constraint conditions were considered for the outer diameter of the plate in conjunction with an internal rigid core. The characterization of this model allows to define the stiffness matrix terms of a custom composite bolted joint finite element, that is the object of future developments of this work. Results of the original proposed method are presented and compared to those obtained by means of FEA performed with a refined reference model, demonstrating a good agreement

Software for evaluating probability-based integrity of reinforced concrete structures

In recent years, much research work has been carried out in order to obtain a more controlled durability and long-term performance of concrete structures in chloride containing environment. In particular, the development of new procedures for probability-based durability design has proved to give a more realistic basis for the analysis. Although there is still a lack of relevant data, this approach has been successfully applied to several new concrete structures, where requirements to a more controlled durability and service life have been specified. A probability-based durability analysis has also become an important and integral part of condition assessment of existing concrete structures in chloride containing environment. In order to facilitate the probability-based durability analysis, a software named DURACON has been developed, where the probabilistic approach is based on a Monte Carlo simulation. In the present paper, the software for the probability-based durability analysis is briefly described and used in order to demonstrate the importance of the various durability parameters affecting the durability of concrete structures in chloride containing environment

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Adaptive chaotic particle swarm algorithm for isogeometric multi-objective size optimization of FG plates

An effective multi-objective optimization methodology that combines the isogeometric analysis (IGA) and adaptive chaotic particle swarm algorithm is presented for optimizing ceramic volume fraction (CVF) distribution of functionally graded plates (FGPs) under eigenfrequencies. The CVF distribution is represented by the B-spline basis function. Mechanical behaviors of FGPs are obtained with NURBS-based IGA and the recently developed simple first-order shear theory. The design variables are the CVFs at control points in the thickness direction, and the optimization objective is to minimize the mass of structure and maximize the first natural frequency. A recently developed multi-objective adaptive chaotic particle swarm algorithm with high efficiency is employed as an optimizer. All desirable features of the developed approach will be illustrated through four numerical examples, confirming its effectiveness and reliability

Program of Research in Structures and Dynamics

The Structures and Dynamics Program was first initiated in 1972 with the following two major objectives: to provide a basic understanding and working knowledge of some key areas pertinent to structures, solid mechanics, and dynamics technology including computer aided design; and to provide a comprehensive educational and research program at the NASA Langley Research Center leading to advanced degrees in the structures and dynamics areas. During the operation of the program the research work was done in support of the activities of both the Structures and Dynamics Division and the Loads and Aeroelasticity Division. During the period of 1972 to 1986 the Program provided support for two full-time faculty members, one part-time faculty member, three postdoctoral fellows, one research engineer, eight programmers, and 28 graduate research assistants. The faculty and staff of the program have published 144 papers and reports, and made 70 presentations at national and international meetings, describing their research findings. In addition, they organized and helped in the organization of 10 workshops and national symposia in the structures and dynamics areas. The graduate research assistants and the students enrolled in the program have written 20 masters theses and 2 doctoral dissertations. The overall progress is summarized

Smart passive adaptive control of laminated composite plates (through optimisation of fibre orientation)

In the classical laminate plate theory for composite materials, it is assumed that the laminate is thin compared to its lateral dimensions and straight lines normal to the middle surface remain straight and normal to the surface after deformation. As a result, the induced twist which is due to the transverse shear stresses and strains are neglected. Also, this induced twist was considered as an unwanted displacement and hence was ignored. However, in certain cases this induced twist would not be redundant and can be a useful displacement to control the behaviour of the composite structure passively. In order to use this induced twist, there is a need for a modified model to predict the behaviour of laminated composites. A composite normally consists of two materials; matrix and fibres. Fibres can be embedded in different orientations in composite lay-ups. In this research, laminated composite models subject to transfer shear effect are studied. A semi analytical model based on Newton-Kantorovich-Quadrature Method is proposed. The presented model can estimate the induced twist displacement accurately. Unlike other semi analytical model, the new model is able to solve out of plane loads as well as in plane loads. It is important to mention that the constitutive equations of the composite materials (and as a result the induced twist) are determined by the orientation of fibres in laminae. The orientation of composite fibres can be optimised for specific load cases, such as longitudinal and in-plane loading. However, the methodologies utilised in these studies cannot be used for general analysis such as out of plane loading problems. This research presents a model whereby the thickness of laminated composite plates is minimised (for a desirable twist angle) by optimising the fibre orientations for different load cases. In the proposed model, the effect of transverse shear is considered. Simulated annealing (SA), which is a type of stochastic optimisation method, is used to search for the optimal design. This optimisation algorithm is not based on the starting point and it can escape from the local optimum points. In accordance with the annealing process where temperature decreases gradually, this algorithm converges to the global minimum. In this research, the Tsai-Wu failure criterion for composite laminate is chosen which is operationally simple and readily amenable to computational procedures. In addition, this criterion shows the difference between tensile and compressive strengths, through its linear terms. The numerical results are obtained and compared to the experimental data to validate the methodology. It is shown that there is a good agreement between finite element and experimental results. Also, results of the proposed simulated annealing optimisation model are compared to the outcomes from previous research with specific loading where the validity of the model is investigated

Mesh-Free and Finite Element-Based Methods for Structural Mechanics Applications

The problem of solving complex engineering problems has always been a major topic in all industrial fields, such as aerospace, civil and mechanical engineering. The use of numerical methods has increased exponentially in the last few years, due to modern computers in the field of structural mechanics. Moreover, a wide range of numerical methods have been presented in the literature for solving such problems. Structural mechanics problems are dealt with using partial differential systems of equations that might be solved by following the two main classes of methods: Domain-decomposition methods or the so-called finite element methods and mesh-free methods where no decomposition is carried out. Both methodologies discretize a partial differential system into a set of algebraic equations that can be easily solved by computer implementation. The aim of the present Special Issue is to present a collection of recent works on these themes and a comparison of the novel advancements of both worlds in structural mechanics applications