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The finite element method (FEM) is a computational tool widely used to design and analyse  complex structures. Currently, there are a number of different approaches to analysis using the FEM that vary according to the type of structure being analysed: beams and plates may use 1D or 2D approaches, shells and solids 2D or 3D approaches, and methods that work for one structure are typically not optimized to work for another. Finite Element Analysis of Structures Through Unified Formulation deals with the FEM used for the analysis of the mechanics of structures in the case of linear elasticity. The novelty of this book is that the finite elements (FEs) are formulated on the basis of a class of theories of structures known as the Carrera Unified Formulation (CUF). It formulates 1D, 2D and 3D FEs on the basis of the same 'fundamental nucleus' that comes from geometrical relations and Hooke's law, and presents both 1D and 2D refined FEs that only have displacement variables as in 3D elements. It also covers 1D and 2D FEs that make use of 'real' physical surfaces rather than 'artificial' mathematical surfaces which are difficult to interface in CAD/CAE software. Key features: * Covers how the refined formulation can be easily and conveniently used to analyse laminated structures, such as sandwich and composite structures, and to deal with multifield problems * Shows the performance of different FE models through the 'best theory diagram' which allows different models to be compared in terms of accuracy and computational cost * Introduces an axiomatic/asymptotic approach that reduces the computational cost of the structural analysis without affecting the accuracy * Introduces an innovative 'component-wise' approach to deal with complex structures * Accompanied by a website hosting the dedicated software package MUL2 (www.mul2.com) Finite Element Analysis of Structures Through Unified Formulation is a valuable reference for researchers and practitioners, and is also a useful source of information for graduate students in civil, mechanical and aerospace engineering.

\"Present a new, unified approach to both classical and advanced beam theory that is becoming established and recognised globally as the most important contribution to the field in the last quarter of a centuryBeam Structures: Classical and Advanced Theories proposes a new original unified approach to beam theory that includes practically all classical and advanced models for beams and which has become established and recognised globally as the most important contribution to the field in the last quarter of a century. This approach overcomes the problem of classical formulae that require different formulas for tension, bending, shear and torsion; it can be applied to any beam geometries and loading conditions, reaching a high level of accuracy, and can tackle problems that in most cases are solved by employing plate/shell and 3D formulations.Beam Structures: Classical and Advanced Theories presents both the classical and advanced beam theories in a form that is very suitable for computer implementation It is accompanied by dedicated software MUL2 that is used to obtain the numerical solutions in the book, allowing the reader to reproduce the examples given in the book as well as to solve other problems of their own. The authors also include a number of static and dynamic problems and solutions that serve to further illustrate the advanced theories presented\"--

\"Plates and Shells for Smart Structures firstly gives an overview of classical plate and shell theories for piezoelectric elasticity, demonstrating their limitations in static and dynamic analysis with a number of example problems. The authors then go on to explain how these limitations can be overcome with the use of the more advanced models that have been developed in recent years; introducing theories able to consider electromechanical couplings as well as those that provide appropriate interface continuity conditions for both electrical and mechanical variables. They provide both analytical and finite element solutions, thus enabling the reader to compare the strong and weak solutions to problems.Plates and Shells for Smart Structures is accompanied by dedicated software MUL2 that is used to obtain the numerical solutions in the book, allowing the reader to reproduce the examples given in the book as well as to solve other problems of their own\"--

This paper provides an overview of the modeling approaches adopted over the years to develop shell theories for composite structures. Furthermore, it presents a method to assess any structural theory concerning the accuracy and computational efficiency and trigger informed decisions on the structural theory to use for a given problem. This method exploits the synergies between the Carrera unified formulation and the axiomatic/asymptotic method. Typical outcomes are the best theory diagrams or the estimation of accuracy of a theory as compared to quasi-3D solutions. The proposed framework can be useful to provide guidelines on the construction of structural theories and can serve as a trainer for the deep learning of neural networks.

This work is a sequel of a previous author's article: \"Theories and Finite Elements for Multilayered. Anisotropic, Composite Plates and Shell\", Archive of Computational Methods in Engineering Vol 9, no 2, 2002; in which a literature overview of available modelings for layered flat and curved structures was given. The two following topics, which were not addressed in the previous work, are detailed in this review: 1. derivation of governing equations and finite element matrices for some of the most relevant plate/shell theories; 2. to present an extensive numerical evaluations of available results, along with assessment and benchmarking. The article content has been divided into four parts. An introduction to this review content is given in Part I. A unified description of several modelings based on displacements and transverse stress assumptions ins given in Part II. The order of the expansion in the thickness directions has been taken as a free parameter. Two-dimensional modelings which include Zig-Zag effects, Interlaminar Continuity as well as Layer-Wise (LW), and Equivalent Single Layer (ESL) description have been addressed. Part III quotes governing equations and FE matrices which have been written in a unified manner by making an extensive use of arrays notations. Governing differential equations of double curved shells and finite element matrices of multilayered plates are considered. Principle of Virtual Displacement (PVD) and Reissner's Mixed Variational Theorem (RMVT), have been employed as statements to drive variationally consistent conditions, e.g.C ^sub z^ ^sup 0^ -Requirements, on the assumed displacements and stransverse stress fields. The number of the nodes in the element has been taken as a free parameter. As a results both differential governing equations and finite element matrices have been written in terms of a few 3×3 fundamental nuclei which have 9 only terms each. A vast and detailed numerical investigation has been given in Part IV. Performances of available theories and finite elements have been compared by building about 40 tables and 16 figures. More than fifty available theories and finite elements have been compared to those developed in the framework of the unified notation discussed in Parts II and III. Closed form solutions and and finite element results related to bending and vibration of plates and shells have been addressed. Zig-zag effects and interlaminar continuity have been evaluated for a number of problems. Different possibilities to get transverse normal stresses have been compared. LW results have been systematically compared to ESL ones. Detailed evaluations of transverse normal stress effects are given. Exhaustive assessment has been conducted in the Tables 28-39 which compare more than 40 models to evaluate local and global response of layered structures. A final Meyer-Piening problem is used to asses two-dimensional modelings vs local effects description.[PUBLICATION ABSTRACT]

In this study, the geometrically nonlinear behaviour caused by large displacements and rotations in the cross sections of thin-walled composite beams subjected to axial loading is investigated. Newton–Raphson scheme and an arc length method are used in the solution of nonlinear equations by finite element method to determine the mechanical effect. The Carrera-Unified formulation (CUF) is used to solve nonlinear, low or high order kinematic refined structure theories for finite beam elements. In the study, displacement area and stress distributions of composite structures with different angles and functionally graded (FG) structures are presented for Lagrange polynomial expansions. The results show the accuracy and computational efficiency of the method used and give confidence for new research.

The present paper assessed the use of variable kinematic two-dimensional elements in the dynamic analysis of Lamb waves propagation in an isotropic plate with piezo-patches. The multi-field finite element model used in this work was based on the Carrera Unified Formulation which offers a versatile application enabling the model to apply the desired order theory. The used variable kinematic model allowed for the kinematic model to vary in space, thereby providing the possibility to implement a classical plate model in collaboration with a refined kinematic model in selected areas where higher order kinematics are needed. The propagation of the symmetric (S0) and the antisymmetric (A0) fundamental lamb waves in an isotropic strip was considered in both mechanical and piezo-elastic plate models. The convergence of the models was discussed for different kinematics approaches, under different mesh refinement, and under different time steps. The results were compared to the exact solution proposed in the literature in order to assess and further determine the effects of the different parameters used when dynamically modeling a Lamb wave propagating in such material. It was shown that the higher order kinematic models delivered a higher accuracy of the propagating wave evaluated using the corresponding Time Of Flight (TOF). Upon using the appropriate mesh refinement of 2000 elements and sufficient time steps of 4000 steps, the error between the TOF obtained analytically and numerically using a high order kinematics was found to be less than 1% for both types of fundamental Lamb waves S0 and A0. Node-dependent kinematics models were also exploited in wave propagation to decrease the computational cost and to study their effect on the accuracy of the obtained results. The obtained results show, in both the mechanical and the piezo-electric models, that a reduction in the computational cost of up to 50% can be easily attained using such models while maintaining an error inferior to 1%.

This paper proposes a performance analysis of a medium-range airliner powered by liquid hydrogen (LH2) propulsion. The focus is on operating performance in terms of achievable payload and range. A non-conventional box-wing architecture was selected to maximize operating performance. An optimization-based multidisciplinary design framework was developed to retrofit a baseline medium-range box-wing aircraft by designing and integrating the fuel tanks needed to store the LH2; several solutions were investigated for tank arrangement and layout by means of sensitivity analyses. As a main outcome, a performance analysis of the proposed LH2-powered box-wing aircraft is provided, highlighting the impact of the introduction of this energy carrier (and the integration of the related tank systems) on aircraft operating performance; a comparative study with respect to a competitor LH2-retrofitted tube-and-wing aircraft is also provided, to highlight the main possible operating differences between the two architectures. The findings reveal that the retrofitted box-wing can achieve long-range flights at the cost of a substantially reduced payload, mainly due to the volume limitations imposed by the installation of LH2 tanks, or it can preserve payload capacity at the expense of a significant reduction in range, as the trade-off implies a reduction in on-board LH2 mass. Specifically, the studied box-wing configuration can achieve a range of 7100 km transporting 150 passengers, or shorter ranges of 2300 km transporting 230 passengers. The competitor LH2-retrofitted tube-and-wing aircraft, operating in the same category and compatible with the same airport apron constraints, could achieve a distance of 1500 km transporting 110 passengers.

In this paper a new plate finite element (FE) for the analysis of composite and sandwich plates is proposed. By making use of the node-variable plate theory assumptions, the new finite element allows for a simultaneous analysis of different subregions of the problem domain with different kinematics and accuracy, in a global/local sense. In particular higher-order theories with an Equivalent-Single-Layer (ESL) approach are simultaneously used with advanced Layer-Wise (LW) models. As a consequence, the computational costs can be reduced drastically by assuming refined theories only in those zones/nodes of the structural domain where the resulting strain and stress states present a complex distribution. On the contrary, computationally cheaper, low-order kinematic assumptions can be used in the remaining parts of the plate where a localized detailed analysis is not necessary. The primary advantage of the present variable-kinematics element and related global/local approach is that no ad-hoc techniques and mathematical artifices are required to mix the fields coming from two different and kinematically incompatible adjacent elements, because the plate structural theory varies within the finite element itself. In other words, the structural theory of the plate element is a property of the FE node in this present approach, and the continuity between two adjacent elements is ensured by adopting the same kinematics at the interface nodes. According to the Unified Formulation by Carrera, the through-the-thickness unknowns are described by Taylor polynomial expansions with ESL approach and by Legendre polynomials with LW approach. Furthermore, the Mixed Interpolated Tensorial Components (MITC) method is employed to contrast the shear locking phenomenon. Several numerical investigations are carried out to validate and demonstrate the accuracy and efficiency of the present plate element, including comparison with various closed-form and FE solutions from the literature .

This paper proposes a novel experimental investigation based on 3D printing to validate numerical models for biomechanics simulations. Soft elastomeric materials have been used in Polyjet multi-material 3D printer to mimicking arteries affected by atherosclerotic plaque. The nonlinear mechanical properties of five digital materials are characterized and used as an input for finite element (FE) modeling. Pressurized air is applied to the internal cavity of the printed model to reproduce the internal blood pressure in the artery. Digital Imaging Correlation is adopted to measure the displacement and deformation. A 1D linear higher-order FE model based on the Carrera Unified Formulation is compared to 3D nonlinear FE solutions.