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This article shows that the governing equations of any plate theory can be directly obtained by manipulating the three-dimensional (3D) equilibrium indefinite equations. Stress components are transformed into plate stress resultants by implementing a few steps proposed in this article. Such a manipulation is shown for simple and complex deformation states. Various known plate theories are considered, such as membrane and bending ones. The most general equations are obtained by referring to higher-order theories based on the Carrera Unified Formulation. To show the method's effectiveness, the differential equations of known (Reissner–Mindlin, Hildelbrand–Reissner–Thomas) and unprecedented plate theories are derived by simply working on the 3D-equilibrium equations. The introduced manipulation consists of the following steps: (1) The 3D equilibrium elasticity is formally written for each of the degrees of freedom of the considered plate theories; (2) the stress resultants are used to replace stress components in the latter equations; (3) the derivatives of the stress components along the plate reference surface coordinate x, y do not affect the nature of the indefinite equilibrium equations, and these derivatives are directly moved to the related stress resultants; (4) the derivatives over the thickness coordinate z should: (i) change the sign of the related stress resultants and (ii) be applied to the base functions of z used to define the stress resultants (as well as the assumption for the displacement along the thickness). In conclusion, this article presents a straightforward method that can effectively replace the use of Newton and Lagrange methods to derive the equilibrium equations of any plate theory. The four steps introduced in this article demonstrate the simplicity and efficiency of this approach. [ABSTRACT FROM AUTHOR]

This study analyzed pretension membranes, focusing on high-order effects. Using a combination of the Carrera Unified Formulation (CUF) and the finite element method, the research employs the unique framework of CUF to integrate innovative structural theories in a seamlessly scalable way. The analysis methodically explores the complex effects of shear and bending stiffness on crucial factors such as thickness, geometry, and materials. A comprehensive numerical examination of the subject is undertaken on numerous cases, and the assessment includes established analytical solutions as well as findings provided by commercial software tools. Particular emphasis is placed on mode aberration, underscoring the critical need for more refined structural models. Furthermore, the results show the crucial role of adopting high-order theory in the dynamic analysis of membrane structure, especially for application in space. [ABSTRACT FROM AUTHOR]

The dynamic response of various rotating stiffened cylindrical and disk structures has been performed using low- and high-fidelity two-dimensional finite element models. The methodology is based on the Carrera Unified Formulation, in which the shell models are obtained hierarchically and automatically. These theories are formulated by expanding the unknown variables over the shell thickness. Various shell models can be implemented depending on the choice of the polynomial employed in the expansion. Lagrange polynomials are considered for developing different kinematic models and for easily modeling the stiffeners. The stiffener deformation is precisely captured through higher-order models, and the mechanical continuity between the stiffeners and skin is automatically guaranteed at the Lagrange points. The linearized equations of motion include the Coriolis and initial stress contributions. Stiffened cylinders and disks with different boundary conditions are considered. The results are compared with the three-dimensional finite element solutions from the literature or obtained using commercial software. [ABSTRACT FROM AUTHOR]

The present work investigates the residual deformations arising from the curing process of composite curved parts and mitigation strategies to reduce them. Numerical simulations based on finite elements and refined structural theories are adopted and verified against closed-form solutions. The higher-order structural theories are based on the Carrera Unified Formulation, and one-dimensional models are built using layer-wise kinematics. The Cure-Hardening Instantaneously Linear Elastic constitutive model is used. The analytical formulation includes the effects of the final demolding and the in-plane deformations. Results consider spring-in and warping angles after the tool removal. The numerical efficiency of the one-dimensional model allows for thorough parametric analyses, and all the possible combinations of an eight-layer cross-ply laminate are considered. The results confirm that the in-plane deformation and the final demolding play a fundamental role in process-induced deformations. Furthermore, deformations can be significantly reduced by considering asymmetric laminates and localized composite patches. [ABSTRACT FROM AUTHOR]

This paper presents a multi-dimensional variable-kinematics finite element model for nonlinear static analyses of structures with complex geometries. The approach incorporates higher-order beam models and classical solid finite elements in a unified framework, enabling refined modeling of complex geometries. The finite element procedure proposed follows the Carrera Unified Formulation (CUF) and uses a pure displacement-based methodology. The governing equations are derived within the classical continuum mechanics framework, and weak-form equilibrium equations are established using the Principle of Virtual Displacements (PVD). Within the CUF framework, higher-order beam and hexahedral solid models are defined in a unified manner, and the governing equations are written in terms of invariants of mathematical models used and the theory of structures approximation. A coupling technique is used between the beam and solid elements at the nodal level using superposition. The capabilities of fully nonlinear variable-kinematics models are investigated for the static analysis of various rectangular and curved structures. The numerical results are compared with solutions obtained using commercial software. Finally, the proposed methodology is applied to analyze more complex geometries in engineering applications. The results show the capabilities of variable-kinematics models in terms of both accuracy and computational efficiency for the computation of highly nonlinear deformed states and localized phenomena, such as stress concentrations and buckling. [ABSTRACT FROM AUTHOR]

In this work, the wave propagation of Rayleigh type through a periodic elastic element covered with a T-plate is analyzed. Viscous-spring artificial boundaries are used to satisfy boundary conditions of a periodic structure. By using the Carrera Unified Formulation (CUF), the various kinematics of the three-dimensional structure are consistently expressed and the propagation of waves within the model is obtained. Lagrange expansion is employed to generate the mathematical model of the structure. The numerical evaluation and the comparison with the results obtained by the analytical method and COMSOL involving different structures reveal that the results of this study are reliable and show that the model developed provides accurate results for the analysis of the periodic elastic structure of T-plates. [ABSTRACT FROM AUTHOR]

Higher order equivalent layer and layer-wise models of elastic composite sandwich toroidal shells are developed using the Unified Carrera Formulation. Also, axisymmetric shell fixed at the ends is considered in detail. Numerical calculations are performed using the computer algebra software Mathematica 14.0. The results of calculation can be used as benchmark examples for finite element analysis of higher order composite sandwich toroidal shells. [ABSTRACT FROM AUTHOR]

Here, an analytical form Navier solution for higher-order micropolar theory of cylindrical shell was developed based on the CUF approach. The cases of complete linear expansion and model based on Timoshenko-Mindlin shear deformation hypothesis are considered in detail. The two-dimensional system of differential equations obtained here using the principle of virtual displacements for the theory of micropolar elastic cylindrical shell of a higher order is solved here for the case of freely supported cylindrical shell using the Navier variable separation method. Some numerical examples were performed and the influence of the rotational field, as well as the micropolar couple stress on the stress–strain state, was analyzed. The equations presented here can be used for the stress–strain calculation and for thin-walled structures modeling in macro-, micro-, and nanoscale, with considering effects of micropolar couple stress and rotation. [ABSTRACT FROM AUTHOR]

Summary: This work proposes a higher‐order unified shell finite element for the analysis of cylinders made of compressible and nearly incompressible hyperelastic materials. The nonlinear governing equations are derived employing the Carrera unified formulation (CUF), thanks to which it is possible to build shell elements with the capability to capture three‐dimensional (3D) transverse and out‐of‐plane effects. The material and geometric nonlinearities are expressed in an orthogonal curvilinear reference system and the coupled formulation of hyperelastic constitutive law is considered. The principle of virtual work and a total Lagrangian approach is used to derive the nonlinear governing equations, which are solved by a Newton–Raphson scheme. The numerical investigations deal with a curved arch and both thick and thin cylinders subjected to line and point loadings. The obtained results are validated by comparing them with those from the literature. They demonstrate the reliability of the proposed method to analyze compressible and incompressible hyperelastic shell structures. [ABSTRACT FROM AUTHOR]

Here, higher order models of elastic shells of revolution are developed using the variational principle of virtual power for 3-D equations of the linear theory of elasticity and generalized series in the coordinates of the shell thickness. Following the Carrera Unified Formulation (CUF), the stress and strain tensors, as well as the displacement vector, were expanded into series in terms of the coordinates of the shell thickness. As a result, all the equations of the theory of elasticity were transformed into the corresponding equations for the expansion coefficients in a series in terms of the coordinates of the shell thickness. All equations for shells of revolution of higher order are developed and presented here for cases whose middle surfaces can be represented analytically. The resulting equations can be used for theoretical analysis and calculation of the stress-strain state, as well as for modeling thin-walled structures used in science, engineering, and technology. [ABSTRACT FROM AUTHOR]

Distyly, a floral dimorphism that promotes outcrossing, is controlled by a hemizygous genomic region known as the S‐locus. Disruptions of genes within the S‐locus are responsible for the loss of distyly and the emergence of homostyly, a floral monomorphism that favors selfing. Using whole‐genome resequencing data of distylous and homostylous individuals from populations of Primula vulgaris and leveraging high‐quality reference genomes of Primula we tested, for the first time, predictions about the evolutionary consequences of transitions to selfing on S‐genes. Our results reveal a previously undetected structural rearrangement in CYPᵀ associated with the shift to homostyly and confirm previously reported, homostyle‐specific, loss‐of‐function mutations in the exons of the S‐gene CYPᵀ. We also discovered that the promoter and intronic regions of CYPᵀ in distylous and homostylous individuals are conserved, suggesting that down‐regulation of CYPᵀ via mutations in its promoter and intronic regions is not a cause of the shift to homostyly. Furthermore, we found that hemizygosity is associated with reduced genetic diversity in S‐genes compared with their paralogs outside the S‐locus. Additionally, the shift to homostyly lowers genetic diversity in both the S‐genes and their paralogs, as expected in primarily selfing plants. Finally, we tested, for the first time, long‐standing theoretical models of changes in S‐locus genotypes during early stages of the transition to homostyly, supporting the assumption that two copies of the S‐locus might reduce homostyle fitness. Here, we focus the transition from distyly to homostyly in the common primroses to study the causes and consequences of mating‐system transitions. Using whole‐genome resequencing data, we find that loss‐of‐functions mutations in the CYPT gene is associated with multiple independent transitions to homostyly and that this transitions has consequences in the so‐called distyly S‐locus. Finally, we tested, for the first time, long‐standing theoretical models of changes in S‐locus genotypes during early stages of the transition to homostyly. [ABSTRACT FROM AUTHOR]

This work investigates the dynamic response of various rotating cylindrical structures using low- and high-fidelity one-dimensional (1D) and two-dimensional (2D) finite element models. The adopted mathematical formalism is based on the Carrera Unified Formulation (CUF). CUF offers a procedure to obtain higher-order beam and shell models hierarchically and automatically. These theories are formulated by expanding the unknown variables over the beam cross-section or along the shell thickness. Various beam and shell models can be implemented depending on the choice of the polynomial employed in the expansion. Both Taylor-like and Lagrange polynomials are considered for developing different kinematic models. The linearized equations of motion include the Coriolis and initial stress contributions. Various thick and thin cylinders and disk structures with different boundary conditions are considered. The beam and shell results are compared with analytical and three-dimensional (3D) finite element (FE) solutions from the literature. [ABSTRACT FROM AUTHOR]

This work presents a numerical method for damage analysis of reinforced concrete beams using the higher-order beam theory based on Carrera unified formulation. The component-wise approach is employed to model the concrete and steel reinforcing bars as two independent one-dimensional finite elements. A modified Mazars damage model with tensile and compressive damage propagation laws is utilized for concrete, and an elastic-perfectly plastic law is used for steel rebars. To address the instability and mesh dependence caused by the strain-softening behavior of concrete, a fracture energy regularization technique based on the crack band model is developed, especially for the higher-order beam theory. The proposed method is validated by comparing its numerical results with three experimental benchmark results. The comparison indicates that the method accurately predicts the damage distribution of concrete and the flexural behavior of RC beams under quasi-static loading conditions while remaining computationally efficient. [ABSTRACT FROM AUTHOR]

In this paper, two-dimensional (2D) structural models are used to analyze thin-walled stiffened structures. A novel approach is presented to model both skins and stiffeners using 2D finite elements (FEs) with enhanced capabilities. The deformation of the stiffeners is accurately described using higher order Lagrange polynomials, and the mechanical continuity between the reinforcements and the skin is automatically ensured in correspondence of the Lagrange points. The 2D FEs are built using the Carrera Unified Formulation (CUF), which allows arbitrary refinement of the stiffener kinematics. In this way, any type of deformation can be described and, if a higher-order model is used, the three-dimensional (3D) stress distribution can be evaluated. The proposed model is tested on a stiffened plate and compared with results obtained using traditional FEA, including 3D and 2D models and a combination of 2D and one-dimensional (1D) models for the stiffeners. The results show and demonstrate the reliability of the proposed method, both in terms of displacements and stresses, when compared to the 3D solution. In addition, the computational cost, evaluated here as the number of degrees of freedom (DOFs), is much lower. Finally, the ability of this model to deal with curved stiffeners is demonstrated with practical examples. [ABSTRACT FROM AUTHOR]

Our study addresses the first boundary value problem in the context of the theory of elastic Cosserat bodies, in its classical form, that is: the motion equations, the initial conditions, and the boundary relations. Then, the variational form is attached to this problem. In this context, the elasticity operator is defined and its properties are proven, the most important of which is that this operator is positive definite. Based on this last property it is possible to prove a result of the existence of a solution for the formulated boundary value problem. Also based on the positive definition of the elasticity operator, is highlighted the possibility of approximating the solution using a variational method. [ABSTRACT FROM AUTHOR]

This work investigates the interactions between the soil and a superstructure subjected to various seismic waves using variable-kinematics finite beam elements. Artificial boundary conditions based on springs and dashpots with appropriate elastic and viscous coefficients were adopted to ensure the absorption of the incident waves and simulate the infinite domain condition. The one-dimensional finite element formulation is obtained with a unified formalism that enables arbitrary structural models to be adopted. Lagrange-type expansions have been used in this work to approximate the beam kinematics and facilitate the application of artificial boundary conditions. Both pressure and shear waves with different incidence angles have been considered, and the dynamic responses calculated with the current approach have been compared with analytical solutions when available. The results have demonstrated the accuracy and potentialities of the methodology and provided reasonable confidence for future applications. [ABSTRACT FROM AUTHOR]

Here, higher order models of elastic composite multilayer shells of revolution are developed using the variational principle of virtual power for the 3-D linear anisotropic theory of elasticity and generalized series in the shell thickness coordinates. Following the Unified Carrera Formula (CUF), the stress and strain tensors, as well as the displacement vector, were expanded into series in terms of the coordinates of the shell thickness. The higher-order cylindrical shell supported on the edges under axisymmetric loading, is considered and solved analytically using a Navier close form solution method. Also, composite axisymmetric circular plated as well as parabolic, hyperbolic and pseudo-spheric shell fixed ate the ends are considered. Numerical calculations were performed using the computer algebra software Mathematica. The resulting equations can be used for theoretical analysis and calculation of the stress-strain state, as well as for modeling thin-walled structures used in science, engineering, and technology. The results of calculation can be used as benchmark examples for finite element analysis of the higher order elastic shells. [ABSTRACT FROM AUTHOR]

This work proposed the use of the Carrera Unified Formulation (CUF) for the vibration and buckling analysis of structures subjected to thermal loads. In detail, the variation of natural frequencies for progressively large thermal loads is investigated. Here, particular attention is focused on the study of buckling thermal loads as degenerate cases of the vibration analysis and on the mode aberration caused by thermal stresses. From this standpoint, the use of CUF for the development of high-order beam and plate models is fundamental. Indeed, Lagrange-like (LE) polynomials are considered for developing the kinematic expansion and Layerwise (LW) theories are employed to characterize the complex phenomena that may appear in composite structures. A linearized formulation to study the natural frequencies variation as a function of the progressive increasing thermal loadings is adopted. Different isotropic and laminated composite structures have been analyzed and compared with the Abaqus solution to validate the presented methodology and provide some benchmark solutions. In addition, a parametric study was conducted to evaluate the stacking sequence and thickness effect in the vibration modes and thermal buckling loads. The results document the excellent accuracy and reliability of the presented methodology and show the potentialities of this numerical tool able to analyze cases that are difficult to study experimentally. [ABSTRACT FROM AUTHOR]

Based on the Carrera unified formulation (CUF) and first-invariant hyperelasticity, this work proposes a displacement-based high order one-dimensional (1 D) finite element model for the geometrical and physical nonlinear analysis of isotropic, slightly compressible soft material structures. Different strain energy functions are considered and they are decomposed in a volumetric and an isochoric part, the former acting as penalization of incompressibility. Given the material Jacobian tensor, the nonlinear governing equations are derived in a unified, total Lagrangian form by expanding the three-dimensional displacement field with arbitrary cross-section polynomials and using the virtual work principle. The exact analytical expressions of the elemental internal force vector and tangent matrix of the unified beam model are also provided. Several problems are addressed, including uniaxial tension, bending of a slender structure, compression of a three-dimensional block, and a thick pinched cylinder. The proposed model is compared with analytical solutions and literature results whenever possible. It is demonstrated that, although 1 D, the present CUF-based finite element can address simple to complex nonlinear hyperelastic phenomena, depending on the theory approximation order. [ABSTRACT FROM AUTHOR]

Here, we present a Navier close form solution method for some type of the higher-order theories for elastic shells of revolution developed using the CUF approach. The higher-order models of elastic shells of revolution are developed using the variational principle of virtual power for 3-D equations of the linear theory of elasticity and generalized series in the coordinates of the shell thickness. The higher-order cylindrical supported on the edges and axisymmetric shells, as well as the shallow spherical shells with rectangular planform, are considered. Numerical calculations were performed using the computer algebra software Mathematica. The resulting equations can be used for theoretical analysis and calculation of the stress–strain state, as well as for modeling thin-walled structures used in science, engineering, and technology. The numerical results can be used as benchmark examples for finite element analysis of the higher-order elastic shells. [ABSTRACT FROM AUTHOR]

Here, higher order models of elastic shells of revolution are developed using the variational principle of virtual power for 3-D equations of the linear theory of elasticity and generalized series in the coordinates of the shell thickness. Following the Unified Carrera Formula (CUF), the stress and strain tensors, as well as the displacement vector, are expanded into series in terms of the coordinates of the shell thickness. As a result, all the equations of the theory of elasticity are transformed into the corresponding equations for the expansion coefficients in a series in terms of the coordinates of the shell thickness. All equations for shells of revolution of higher order are developed and presented here for cases whose middle surfaces can be represented analytically. The resulting equations can be used for theoretical analysis and calculation of the stress–strain state, as well as for modeling thin-walled structures used in science, engineering, and technology. [ABSTRACT FROM AUTHOR]

This work intends to present a novel numerical approach for studying the vibration behaviours of variable angle tow (VAT) composite structures in their quasi-static nonlinear equilibrium states. This methodology is able to predict the buckling load, to investigate the natural frequencies variation for progressively higher loads, and to provide a means for verifying experimental Vibration Correlation Technique results. The use of VAT composites, in which the fibre orientations are allowed to vary along with a curvilinear pattern within each lamina, dramatically increases the design space and provides a significant improvement in buckling performance and benefits in the postbuckling regime. This study has been performed using an innovative methodology based on the well-established Carrera Unified Formulation able to describe several kinematic models for two-dimensional structures. In detail, layerwise theories are employed to characterize the complex phenomena that may appear in VAT composite structures. All Green-Lagrange strain components are employed because far nonlinear regimes are investigated. Furthermore, the geometrical nonlinear equations are written in a total Lagrangian framework and solved with an opportune Newton–Raphson method along with a path-following approach based on the arc-length constraint. Different VAT composite structures have been analyzed to validate the proposed approach and provide some benchmark solutions. The computed equilibrium paths are compared with results obtained using the commercial code ABAQUS. The results document the good accuracy and reliability of the presented methodology and show this numerical tool's potentialities. [ABSTRACT FROM AUTHOR]

It is shown that the classical theories of micropolar plates and shells can be obtained using the Carrera Unified Formulation (CUF) approach as a special case of approximation. The theory of micropolar plates and shells based on the hypotheses of Timoshenko–Mindlin and Kirchhoff–Love is considered in detail. The stress and strain tensors, as well as the displacement and rotation vectors are presented as linear expansion along the shell thickness coordinates. Then, all the equations of the micropolar theory of elasticity (including the generalized Hooke's law) were transformed into the corresponding equations for the expansion coefficients in the coordinates of the shell thickness. All equations of the theory of micropolar plates and shells based on the hypotheses of Timoshenko–Mindlin and Kirchhoff–Love are presented here. Micropolar plates in Cartesian and polar coordinates, as well as micropolar shells of cylindrical, conical, spherical and shallow geometry are considered in detail. The equations obtained can be used to calculate the stress-strain state and simulate thin-walled structures at the macro, micro and nanoscale, taking into account the micropolar stresses and the effects of rotation. [ABSTRACT FROM AUTHOR]

Starting from the variational principle of virtual power for the three-dimensional equations of the micropolar theory of elasticity and using generalized series in terms of the plate thickness coordinates a new higher order models of orthotropic micropolar plates have been developed here for the first time. Following carrera unified formulation, the stress and strain tensors, as well as the vectors of displacements and rotation, have been expanded into series in terms of the plate thickness coordinates. Then, all the equations of the micropolar theory of elasticity (including generalized Hooke's law) have been transformed to the corresponding equations for the coefficients of the series expansion on the plate thickness coordinates. A system of differential equations in terms of the displacements and rotation vectors and natural boundary conditions for the coefficients of the series expansion of the plate thickness coordinates have been obtained in the same way as in the classical theory of elasticity. All equations for the higher order theory of micropolar plates have been developed and presented here. The case of complete linear expansion has been considered in detail and compared with the theories based on shear deformation and Kirchhoff hypothesis. The obtained equations can be used for calculating the stress-strain and for modeling thin walled structures in macro, micro, and nanoscale when taking into account micropolar couple stress and rotation effects. [ABSTRACT FROM AUTHOR]

A new multi-field beam model based on Carrera's Unified Formulation (CUF) is offered in this article to efficiently solve the hygro-thermal-mechanical problem of beam structures with high-fidelity. Several beam models have been hierarchically derived in the framework of CUF with consideration of the hygro-thermal stresses. By adopting the principle of virtual displacement, the element stiffness matrix can be derived into a compact form. The temperature and humidity profile is generated from the Fourier's heat conduction and Fick's law, respectively. With simply supported and cantilever configurations being adopted, hygro-mechanical and hygro-thermal-mechanical analyses are carried out for different beam slenderness ratios. Results are provided in terms of three-dimensional displacement and stress distributions. The proposed one-dimensional CUF-based beam model has been validated against traditional three-dimensional FEM-based solutions, and an excellent correlation has been achieved. It is found that an accurate result can be obtained through the proposed CUF-based beam model with reduced computational costs. [ABSTRACT FROM AUTHOR]

In this research, the mechanism of energy dissipation in viscoelastic materials is presented by extracting time-dependent displacement and stress–strain distribution analysis in a beam, which contains a viscoelastic part. The structure is discretized into finite beam elements, the kinematic theory of which is based on Carrera unified formulation using Lagrange expansion on the cross section. For the viscoelastic contribution, the integral form of viscoelastic constitutive law in which the stress is related to the integral form of the viscous module and the strain rate is executed. The governing equations of the finite element model of the structure are derived using Hamilton's principle, and to avoid the computational cost of convolution integral, we have exploited the Laplace transform to the three-dimensional displacement, stress, and strain fields. Finally, the results are transformed to the time domain using numerical inversion methods. A numerical model that has been validated with the results in the literature is considered. To highlight the depreciating consequence of the viscoelastic material, simulation of the multi-layered beam that is isotropic and elastic in all parts except for a certain part that contains the viscoelastic contribution is undertaken, and the temporal response and the stress–strain fields are extracted and discussed. As a result, extreme variations in stress distribution in the location of viscoelastic contributions, hysteresis stress–strain, and changes in beam temporal history to viscoelastic contribution displacement have been observed. [ABSTRACT FROM AUTHOR]

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In this paper, the use of the node-dependent kinematics concept for the geometrical nonlinear analysis of composite one-dimensional structures is proposed With the present approach, the kinematics can be independent in each element node. Therefore the theory of structures changes continuously over the structural domain, describing remarkable cross-section deformation with higher-order kinematics and giving a lower-order kinematic to those portion of the structure which does not require a refinement. In this way, the reliability of the simulation is ensured, keeping a reasonable computational cost. This is possible by Carrera unified formulation, which allows writing finite element nonlinear equilibrium and incremental equations in compact and recursive form. Compact and thin-walled composite structures are analyzed, with symmetric and unsymmetric loading conditions, to test the present approach when dealing with warping and torsion phenomena. Results show how finite element models with node-dependent behave as well as ones with uniform highly refined kinematic. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by node-dependent kinematics analysis. [ABSTRACT FROM AUTHOR]

In our paper, we consider the mixed problem in the context of the Green-Naghdi theory of thermoelastic Cosserat media. Using very accessible mathematical calculations, we prove two qualitative results on the solutions of the formulated mixed problem. Thus, in the first of these approaches, we obtain a result of stability, of the Hölder type, with regards to the loads. In the second main result, we prove a continuous dependence result regarding the initial values from the mixed problem. It should be noted that we obtain these results without imposing very restrictive conditions on the thermoelastic tensors in the constitutive equations. In fact, imposed restrictions are commonly used in Mechanics of Continuous Media. [ABSTRACT FROM AUTHOR]

This article discusses the potential role of ancestry in mutations associated with non-alcoholic fatty liver disease (NAFLD) and hepatocellular carcinoma (HCC) in Latin Americans. Latin America has a diverse population with varying proportions of genomes from different continental ancestries. The study evaluated data from 429 individuals with HCC from six Latin American countries and found that NAFLD-HCC was more common in patients of non-European descent compared to those of European descent. However, the study used self-reported heritage to define ancestry, which may introduce bias. Further research is needed to better understand the interaction between ancestry and liver disease. [Extracted from the article]

New higher-order models of orthotropic micropolar plates and shells have been developed using Carrera Unified Formulation (CUF). Here, a complete linear expansion case (CLEC) has been considered in detail. The stress and strain tensors, as well as the vectors of displacements and rotation, have been presented as linear expansion in terms of the shell thickness coordinates. Then, all the equations of the micropolar theory of elasticity (including generalized Hooke's law) have been transformed to the corresponding equations for the coefficients of the expansion on the shell thickness coordinates. A system of differential equations in terms of the displacements and rotation vectors and natural boundary conditions for the coefficients of the expansion of the shell thickness coordinates has been obtained. All equations for the case of CLEC theory of micropolar plates and shells have been developed and presented here. The obtained equations can be used for calculating the stress-strain and for modeling thin walled structures in macro, micro, and nanoscale when taking into account micropolar couple stress and rotation effects. [ABSTRACT FROM AUTHOR]

Starting from the variational principle of virtual power for the 3-D equations of the micropolar theory of elasticity in orthogonal curvilinear coordinates and using generalized series in terms of the plate thickness coordinates a new higher order model of orthotropic micropolar plates and shells have been developed here. Following Carrera Unified Formulation (CUF), the stress and strain tensors, as well as the vectors of displacements and rotation, have been expanded into series in terms of the shell thickness coordinates. Then, all the equations of the micropolar theory of elasticity (including generalized Hooke's law) have been transformed to the corresponding equations for the coefficients of the series expansion on the plate thickness coordinates. A system of differential equations in terms of the displacements and rotation vectors and natural boundary conditions for the coefficients of the series expansion of the shell thickness coordinates have been obtained in the same way as in the classical theory of elasticity. All equations for the higher order theory of micropolar plates and shells have been developed and presented here. The obtained equations can be used for calculating the stress-strain and for modeling thin walled structures in macro, micro, and nanoscale when taking into account micropolar couple stress and rotation effects. [ABSTRACT FROM AUTHOR]

This paper presents numerical results concerning the nonlinear analysis of thin-walled isotropic structures via 1 D structural theories built with the Carrera Unified Formulation (CUF). Both geometrical and material nonlinearities are accounted for, and square, C- and T-shaped beams are considered. The results focus on equilibrium curves, displacement, and stress distributions. Comparisons with literature and 3 D finite elements (FE) are provided to assess the formulation's accuracy and computational efficiency. It is shown how 1 D models based on Lagrange expansions of the displacement field are comparable to 3 D FE regarding the accuracy but require considerably fewer degrees of freedom. [ABSTRACT FROM AUTHOR]

In this work, a unified formulation of full geometrically nonlinear refined shell theory is developed for the accurate analysis of highly flexible shell structures. The tensor calculus is utilized to explicitly derive the linear and nonlinear differential operator matrices of the geometrical relation in the orthogonal parallel curvilinear coordinate system. By employing the Carrera Unified Formulation (CUF), various kinematics of two-dimensional shell structures are consistently formulated via an appropriate index notation and a generalized expansion of the primary variables by arbitrary functions in the thickness direction, leading to lower- to higher-order shell models with only pure displacement variables. Furthermore, the principle of virtual work and a finite element approximation are exploited to straightforwardly formulate the nonlinear governing equations in a total Lagrangian approach. Particularly, the path-following Newton–Raphson linearization method based on the arc-length constraint is used to deal with the full geometrically nonlinear problem. Independent of the theory approximation order, the forms of the fundamental nuclei of the secant and tangent stiffness matrices of the unified shell element are formulated via the CUF and the three-dimensional Green-Lagrange strain components. Numerical assessments and comparisons of the present results with those provided in the literature for popular benchmark problems involving different metallic shell structures are found to be excellent and demonstrate the capabilities of the developed CUF shell model to predict the post-buckling, large-deflection, snap-through and snap-back nonlinear responses with high accuracy. [ABSTRACT FROM AUTHOR]

This paper deals with finite element analysis of helicopter blades with single and double swept geometries made by metallic and composite materials. First, classical and refined beam theories are combined at the element level via a nodedependent kinematic (NDK) concept, which was recently introduced by the authors. Such an NDK approach enables the accuracy/efficiency ratio of the solution to be tuned according to the level of fidelity required by the design phase. Second, one-dimensional NDK models are combined with the possibility to introduce solid elements in those regions of the blade with a sharp variation of the geometries. The numerical examples consider a swept-tip rectangular beam and a doubleswept helicopter blade with a realistic airfoil. Natural frequencies and through-the-layer stress distributions are reported to demonstrate the flexibility and computational efficiency of the proposed methodology. [ABSTRACT FROM AUTHOR]

The geometrical nonlinear effects caused by large displacements and rotations over the cross section of composite thin-walled structures are investigated in this work. The geometrical nonlinear equations are solved within the finite element method framework, adopting the Newton–Raphson scheme and an arc-length method. Inherently, to investigate cross-sectional nonlinear kinematics, low- to higher-order theories are employed by using the Carrera unified formulation, which provides a tool to generate refined theories of structures in a systematic manner. In particular, beams and shell-like laminated composite structures are analyzed using a layerwise approach, according to which each layer has its own independent kinematics. Different stacking sequences are analyzed, to highlight the influence of the cross-ply angle on the static responses. The results show that the geometrical nonlinear effects play a crucial role, mainly when higher-order theories are utilized. [ABSTRACT FROM AUTHOR]

New higher order models of micropolar beams, which is based on Carrera unified formulation have been developed here. The higher order theory is based on a variational principle of virtual power and the expansion of the 3D equations of the micropolar theory of elasticity into generalized series in terms of cross-section coordinates. The stress and strain tensors, as well as vectors of displacements and rotation, have been expanded into series in terms of cross-section coordinates. Thereby, all equations of the micropolar theory of elasticity (including generalized Hooke's law) have been transformed to the corresponding equations for the coefficients of the series of cross-section coordinates. Then, in the same way, as in the classical theory of elasticity, a system of differential equations in terms of displacements and rotation with boundary conditions for the coefficients of the series of cross-section coordinates have been obtained. All equations for higher order theory of micropolar plates have been developed and presented here. The case of complete linear expansion has been considered in detail. The obtained equations can be used for calculating the stress–strain and for modeling thin walled structures in macro, micro, and nanoscale when taking into account micropolar couple stress and rotation effects. [ABSTRACT FROM AUTHOR]

In the framework of finite elements (FEs) applications, this paper proposes the use of the node-dependent kinematics (NDK) concept to the large deflection and post-buckling analysis of thin-walled metallic one-dimensional (1D) structures. Thin-walled structures could easily exhibit local phenomena which would require refinement of the kinematics in parts of them. This fact is particularly true whenever these thin structures undergo large deflection and post-buckling. FEs with kinematics uniform in each node could prove inappropriate or computationally expensive to solve these locally dependent deformations. The concept of NDK allows kinematics to be independent in each element node; therefore, the theory of structures changes continuously over the structural domain. NDK has been successfully applied to solve linear problems by the authors in previous works. It is herein extended to analyze in a computationally efficient manner nonlinear problems of beam-like structures. The unified 1D FE model in the framework of the Carrera Unified Formulation (CUF) is referred to. CUF allows introducing, at the node level, any theory/kinematics for the evaluation of the cross-sectional deformations of the thin-walled beam. A total Lagrangian formulation along with full Green–Lagrange strains and 2nd Piola Kirchhoff stresses are used. The resulting geometrical nonlinear equations are solved with the Newton–Raphson linearization and the arc-length type constraint. Thin-walled metallic structures are analyzed, with symmetric and asymmetric C-sections, subjected to transverse and compression loadings. Results show how FE models with NDK behave as well as their convenience with respect to the classical FE analysis with the same kinematics for the whole nodes. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by NDK analysis. Remarkable advantages are shown in the analysis of thin-walled structures with transverse stiffeners. [ABSTRACT FROM AUTHOR]

Navier's closed-form solution for the higher order theory of micropolar plates based on the CUF approach has been developed here. Obtained using a principle of virtual displacements the 2D system of the differential equations for the higher order theory of micropolar elastic plates is solved here for the case of simply supported plates using Navier's method of the variables separation. For the higher order theory of micropolar plates developed here, which is based on CUF, some numerical examples have been done and the influence the rotation field on the stress–strain fields has been analyzed. Methods of determination of the classical and micropolar elastic moduli of different materials have been analyzed, and available experimental data have been presented in Nowacki's notations. The obtained equations can be used for calculating the stress–strain and for modeling thin walled structures in macro-, micro- and nanoscale when taking into account micropolar couple stress and rotation effects. [ABSTRACT FROM AUTHOR]

This paper deals with the evaluation of time response analyses of typical aerospace metallic structures. Attention is focussed on detailed stress state distributions over time by using the Carrera Unified Formulation (CUF) for modeling thin-walled reinforced shell structures. In detail, the already established component-wise (CW) approach is extended to dynamic time response by mode superposition and Newmark direct integration scheme. CW is a CUF-based modeling technique which allows to model multi-component structures by using the same refined finite element for each structural component, e.g. stringers, panels, ribs. Component coupling is realized by imposing displacement continuity without the need of mathematical artifices in the CW approach, so the stress state is consistent in the entire structural domain. The numerical results discussed include thin-walled open and closed section beams, wing boxes and a benchmark wing subjected to gust loading. They show that the proposed modeling technique is effective. In particular, as CW provides reach modal bases, mode superposition can be significantly efficient, even in the case of complex stress states. [ABSTRACT FROM AUTHOR]

Summary: Peridynamics is a nonlocal theory which has been successfully applied to solid mechanics and crack propagation problems over the last decade. This methodology, however, may lead to large computational calculations which can soon become intractable for many problems of practical interest. In this context, a technique to couple—in a global/local sense–three‐dimensional peridynamics with one‐dimensional high‐order finite elements based on classical elasticity is proposed. The refined finite elements employed in this work are based on the well‐established Carrera Unified Formulation, which the previous literature has demonstrated to provide structural formulations with unprecedented accuracy and optimized computational efficiency. The coupling is realized by using Lagrange multipliers that guarantee versatility and physical consistency as shown by the numerical results, including the linear static analyses of solid and thin‐walled beams as well as of a reinforced panel of aeronautic interest. [ABSTRACT FROM AUTHOR]

In this article, the mechanical behavior of three-dimensional curved beams is investigated through closed-form solution as well as one-dimensional finite elements based on Carrera's Unified Formulation (CUF). CUF is a hierarchical formulation in which the approximation order of the displacement field is a free parameter of the analysis. Therefore, refined models accounting for higher-order effects such as shear deformation and local warping can be obtained with no need for ad hoc formulations. The principle of virtual displacements (PVD) is used in order to derive both strong and weak formulations. For the latter, locking phenomena typical of curved finite elements are tackled by means of a Mixed Interpolation of Tensorial Components (MITC). Numerical results for different boundary conditions and loading configurations are investigated and validated towards elasticity solutions and commercial software finite elements showing that the proposed formulation can lead to an accurate evaluation of the displacement and stress fields with reduced computational costs. [ABSTRACT FROM AUTHOR]

This paper investigates geometrically nonlinear effects due to large deformations over the cross sections of beam-like and shell-like structures. Finite elements are used to provide numerical solutions along with the Newton–Raphson technique and the arc-length method. Refined theories able to capture cross-sectional deformation are constructed by referring to the Carrera unified formulation. Full nonlinear Green-Lagrange strains and second Piola-Kirchoff stresses are employed in a total Lagrangian scenario. The numerical results demonstrate that geometrical nonlinearities play a fundamental role when cross-sectional deformations become significant and theories of structures with nonlinear kinematics are utilized. In other words, this means that the use of refined beam models may be ineffective if geometrical nonlinear relations are not employed. These phenomena become particularly evident in thin-walled/shell-like type structures. [ABSTRACT FROM AUTHOR]

We studied the characteristics of a phononic crystal which consists of hollow pillars mounted on the surface of semi-infinite substrate. In this study, the existence of surface waves whispering gallery modes referred as localized cavity modes of the hollow pillars at the subwavelength frequency spectrum is reported. The interaction of the hollow pillars with the surface waves induce localized cavity modes and by tuning the inner radius of the hollow pillars these confined modes can be adjusted/tuned inside the bandgap region, thus introducing new applications for the surface waves based phononic crystals and acoustic metamaterial devices. These subwavelength confined cavity modes possess high-q narrow passband characteristics induced by the interaction of cavity modes with the surface waves propagating at the surface of semi-infinite substrate. We demonstrate the subwavelength waveguiding and other functionalities of these localized cavity modes by tuning the inner radius of the hollow pillars and allowing the specific wavelength frequencies to pass through the monochannel, multichannel, and linear cavity based compact waveguides. To make the study more general, we demonstrate the wave multiplexing phenomena for the identical frequencies (diameters of the hollow pillars are kept constant) for all types of waveguides. However, by varying the inner radii of the hollow pillars, the high-q localized frequencies can be tuned. All the physical phenomena presented shows excellent agreement and it indicates promising applications for the manipulation of surface waves in the surface acoustic waves devices, surface waves sensor and actuator technology, and other photonic/phononic and metamaterial applications. [ABSTRACT FROM AUTHOR]

This research work deals with the analysis of elastic shell structures in the large displacement and rotation field adopting one-dimensional (1D) and two-dimensional (2D) unified models. Namely, higher order beam and shell theories accounting for geometrical nonlinearities are formulated by employing a unified framework based on the Carrera unified formulation (CUF) and a total Lagrangian approach. Thus, a finite element (FE) approximation is used along with a Newton-Raphson method and an arc-length path-following approach to perform nonlinear analyses. Low- to higher order beam and shell theories are used to evaluate the nonlinear equilibrium path, and results are compared between the two models, with reference solutions coming from literature or 2D and three-dimensional (3D) models from NASTRAN. Convergence analyses show how CUF 1D models are able to describe the geometrical nonlinear behavior of analyzed structure with a lower number of degrees of freedom (DoFs) than 2D and 3D models. [ABSTRACT FROM AUTHOR]

An exact geometry four-node piezoelectric solid-shell element through the sampling surfaces formulation is proposed. The sampling surfaces formulation is based on choosing inside the shell N – 2 sampling surfaces parallel to the middle surface and located at Chebyshev polynomial nodes to introduce the displacements and electric potentials of these surfaces as fundamental shell unknowns. The bottom and top surfaces are also included into a set of sampling surfaces. Such choice of unknowns with the use of Lagrange polynomials of degree N – 1 in the through-the-thickness interpolations of displacements, strains, electric potential, and electric field yields a robust piezoelectric shell formulation. To implement efficient analytical integration throughout the solid-shell element, the extended assumed natural strain method is employed. The developed hybrid-mixed four-node piezoelectric solid-shell element is based on the Hu-Washizu variational principle and shows the excellent performance for coarse mesh configurations. It can be useful for the 3D stress analysis of piezoelectric shells with variable curvatures, in particular for the modeling and analysis of spiral actuators. [ABSTRACT FROM AUTHOR]

Fluid–structure interaction is fundamental to the characteristics of the induced flows due to the motion of structures in fluids and also is crucial to the performance of submerged structures. This paper presents a three-dimensional analytical study of the intrinsic free vibration of an elastic multilayered hollow sphere interacting with an exterior non-Newtonian fluid medium. The fluid is assumed to be characterized by a compressible linear viscoelastic model accounting for both the shear and compressional relaxation processes. For small-amplitude vibrations, the equations governing the viscoelastic fluid can be linearized, which are then solved by introducing appropriate potential functions. The solid is assumed to exhibit a particular material anisotropy, i.e. spherical isotropy, which includes material isotropy as a special case. The equations governing the anisotropic solid are solved in spherical coordinates using the state-space formalism, which finally establishes two separate transfer relations correlating the state vectors at the innermost surface with those at the outermost surface of the multilayered hollow sphere. By imposing the continuity conditions at the fluid–solid interface, two separate analytical characteristic equations are derived, which characterize two independent classes of vibration. Numerical examples are finally conducted to validate the theoretical derivation as well as to investigate the effects of various factors, including fluid viscosity and compressibility, fluid viscoelasticity, solid anisotropy and surface effect, as well as solid intrinsic damping, on the vibration characteristics of the submerged hollow sphere. Particularly, our theoretically predicted vibration frequencies and quality factors of gold nanospheres with intrinsic damping immersed in water agree exceptionally well with the available experimentally measured results. The reported analytical solution is truly and fully three-dimensional, covering from the purely radial breathing mode to the torsional mode to any general spheroidal mode as well as being applicable to various simpler situations, and hence can be a broad-spectrum benchmark in the study of fluid–structure interaction. [ABSTRACT FROM AUTHOR]

This paper intends to establish a unified theory of structures based on the micropolar elasticity (ME). ME allows taking into consideration the microstructure of the material, through the adoption of four additional material parameters. In this way, the size-effects of the structure can be caught. The proposed model is developed in the domain of the Carrera unified formulation (CUF), according to which theories of structures can degenerate into unknown kinematics that makes use of an arbitrary expansion of the generalized variables. CUF is a hierarchical formulation that considers the order of the structural model as input of the analysis, so that no specific approximation and manipulation is needed to implement refined theories. Different types of structures have been analyzed in the present work, and the results are compared and validated with benchmarks from the literature. The effects of the new material parameters are addressed too, along with the capability of the proposed model to deal with size-effects and high-order structural behaviors. Finally, stress analysis is detailed to further highlight the differences between micropolar and classical elasticity. [ABSTRACT FROM AUTHOR]