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Search results for: FUNCTIONALLY GRADED POROUS NANOPLATES, THREE-DIMENSIONAL ELASTICITY, LARGE DEFLECTIONS, NONLOCAL ELASTICITY, ANALYTICAL METHODS
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Nonlocal three-dimensional theory of elasticity for buckling behavior of functionally graded porous nanoplates using volume integrals
PublicationIn this paper, the buckling of rectangular functionally graded (FG) porous nanoplates based on threedimensional elasticity is investigated. Since, similar researches have been done in two-dimensional analyses in which only large deflections with constant thickness were studied by using various plate theories; therefore, discussion of large deformations and change in thickness of plates after deflection in this study is examined....
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Nonlocal elasticity analysis of moderately thick porous functionally graded plates in a hygro-thermal environment
PublicationThis work performs a novel quasi three-dimensional (3D) bending analysis for a moderately thick functionally graded material (FGM) made of nanoceramics and metal powders, in presence of porosities due to some incorrect manufacturing processes. Such porosities can appear within the plate in two forms, namely, even and uneven distributions. The modeled system assumes a polymer matrix where both shear and transverse factors coexist....
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Implementation of Hermite-Ritz method and Navier’s Technique for Vibration of Functionally Graded Porous Nanobeam Embedded in Winkler-Pasternak Elastic Foundation Using bi-Helmholtz type of nonlocal elasticity
PublicationPresent study is devoted to investigating the vibration characteristics of Functionally Graded (FG) porous nanobeam embedded in an elastic substrate of Winkler-Pasternak type. Classical beam theory (CBT) or Euler-Bernoulli beam theory (EBT) has been incorporated to address the displacement of the FG nanobeam. Bi-Helmholtz type of nonlocal elasticity is being used to capture the small scale effect of the FG nanobeam. Further, the...
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Analiza nieliniowa powłok z materiałów gradientowych w ośrodku mikropolarnym
PublicationW pracy zaprezentowano analizę powłok z materiałów gradientowych dla zakresu dużych przemieszczeń. Macierz konstytutywna została wyprowadzona dla elementu powłokowego o 6 stopniach swobody w węźle w teorii ośrodka mikropolarnego. Zaprezentowano wyniki numeryczne dla swobodnie podpartej kwadratowej płyty FGM i porównano je z wynikami z literatury oraz uzyskanymi w programie Abaqus.
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Thermal buckling of functionally graded piezomagnetic micro- and nanobeams presenting the flexomagnetic effect
PublicationGalerkin weighted residual method (GWRM) is applied and implemented to address the axial stability and bifurcation point of a functionally graded piezomagnetic structure containing flexomagneticity in a thermal environment. The continuum specimen involves an exponential mass distributed in a heterogeneous media with a constant square cross section. The physical neutral plane is investigated to postulate functionally graded material...
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Analytical predictions for the buckling of a nanoplate subjected to non-uniform compression based on the four-variable plate theory
PublicationIn the present study, the buckling analysis of the rectangular nanoplate under biaxial non-uniform compression using the modified couple stress continuum theory with various boundary conditions has been considered. The simplified first order shear deformation theory (S-FSDT) has been employed and the governing differential equations have been obtained using the Hamilton’s principle. An analytical approach has been applied to obtain...
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HYGRO-MAGNETIC VIBRATION OF THE SINGLE-WALLED CARBON NANOTUBE WITH NONLINEAR TEMPERATURE DISTRIBUTION BASED ON A MODIFIED BEAM THEORY AND NONLOCAL STRAIN GRADIENT MODEL
PublicationIn this study, vibration analysis of single-walled carbon nanotube (SWCNT) has been carried out by using a refined beam theory, namely one variable shear deformation beam theory. This approach has one variable lesser than a contractual shear deformation theory such as first-order shear deformation theory (FSDT) and acts like classical beam approach but with considering shear deformations. The SWCNT has been placed in an axial or...
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A novel one-variable first-order shear deformation theory for biaxial buckling of a size-dependent plate based on Eringen’s nonlocal differential law
PublicationPurpose – This paper aims to present a new one-variable first-order shear deformation theory (OVFSDT) using nonlocal elasticity concepts for buckling of graphene sheets. Design/methodology/approach – The FSDT had errors in its assumptions owing to the assumption of constant shear stress distribution along the thickness of the plate, even though by using the shear correction factor (SCF), it has been slightly corrected, the errors...
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A new hyperbolic-polynomial higher-order elasticity theory for mechanics of thick FGM beams with imperfection in the material composition
PublicationA drawback to the material composition of thick functionally graded materials (FGM) beams is checked out in this research in conjunction with a novel hyperbolic‐polynomial higher‐order elasticity beam theory (HPET). The proposed beam model consists of a novel shape function for the distribution of shear stress deformation in the transverse coordinate. The beam theory also incorporates the stretching effect to present an indirect...
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On forced vibrations of piezo-flexomagnetic nano-actuator beams
PublicationThe effect of excitation frequency on the piezomagnetic Euler-Bernoulli nanobeam taking the flexomagnetic material phenomenon into consideration is investigated in this chapter. The magnetization with strain gradients creates flexomagneticity. We couple simultaneously the piezomagnetic and flexomagnetic properties in an inverse magnetization. Resemble the flexoelectricity, the flexomagneticity is also size-dependent. So, it has...
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Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed Piezomagnetic Nanobeams
PublicationWe investigated the stability of an axially loaded Euler–Bernoulli porous nanobeam considering the flexomagnetic material properties. The flexomagneticity relates to the magnetization with strain gradients. Here we assume both piezomagnetic and flexomagnetic phenomena are coupled simultaneously with elastic relations in an inverse magnetization. Similar to flexoelectricity, the flexomagneticity is a size-dependent property. Therefore,...
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A comprehensive study on nonlinear hygro-thermo-mechanical analysis of thick functionally graded porous rotating disk based on two quasi three-dimensional theories
PublicationIn this paper, a highly efficient quasi three-dimensional theory has been used to study the nonlinear hygro-thermo-mechanical bending analysis of very thick functionally graded material (FGM) rotating disk in hygro-thermal environment considering the porosity as a structural defect. Two applied quasi three-dimensional displacement fields are assumed in which the strain along the thickness is not zero unlike most of the other plate...
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Flexomagneticity in Functionally Graded Nanostructures
PublicationFunctionally graded structures have shown the perspective of materials in a higher efficient and consistent manner. This study reports a short investigation by concentrating on the flexomagnetic response of a functionally graded piezomagnetic nano-actuator, keeping in mind that the converse magnetic effect is only taken into evaluation. The rule of mixture assuming exponential composition of properties along with the thickness...
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Characterization of the Functionally Graded Shear Modulus of a Half-Space
PublicationIn this article, a method is proposed for determining parameters of the exponentialy varying shear modulus of a functionally graded half-space. The method is based on the analytical solution of the problem of pure shear of an elastic functionally graded half-space by a strip punch. The half-space has the depth-wise exponential variation of its shear modulus, whose parameters are to be determined. The problem is reduced to an integral...
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Free Vibration of Flexomagnetic Nanostructured Tubes Based on Stress-driven Nonlocal Elasticity
PublicationA framework for the flexomagneticity influence is here considered extending the studies about this aspect on the small scale actuators. The developed model accommodates and composes linear Lagrangian strains, Euler-Bernoulli beam approach as well as an extended case of Hamilton’s principle. The nanostructured tube should subsume and incorporate size effect; however, for the sake of avoiding the staggering costs of experiments,...
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Bending analysis of functionally graded nanoplates based on a higher-order shear deformation theory using dynamic relaxation method
PublicationIn this paper, bending analysis of rectangular functionally graded (FG) nanoplates under a uniform transverse load has been considered based on the modified couple stress theory. Using Hamilton’s principle, governing equations are derived based on a higher-order shear deformation theory (HSDT). The set of coupled equations are solved using the dynamic relaxation (DR) method combined with finite difference (FD) discretization technique...
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Ellipticity in couple-stress elasticity
PublicationWe discuss ellipticity property within the linear couple-stress elasticity. In this theory, there exists a deformation energy density introduced as a function of strains and gradient of macrorotations, where the latter are expressed through displacements. So the couple-stress theory could be treated as a particular class of strain gradient elasticity. Within the micropolar elasticity, the model is called Cosserat pseudocontinuum...
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Analytical Methods
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Wojciech Wojnowski dr inż.
PeopleUkończył V Liceum Ogólnokształcące w Gdańsku w klasie o profilu matematyczno-fizycznym z wykładowym językiem angielskim. W 2009 roku rozpoczął studia na Wydziale Chemicznym PG na kierunku technologia chemiczna, uzyskując w 2012 roku tytuł inżyniera, a w 2013 tytuł magistra. W latach 2013–2015 studiował sinologię na Uniwersytecie w Nankinie dzięki uzyskaniu Stypendium Rządu ChRL. Po powrocie do Polski w 2015 roku rozpoczął studia...
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On Dynamic Boundary Conditions Within the Linear Steigmann-Ogden Model of Surface Elasticity and Strain Gradient Elasticity
PublicationWithin the strain gradient elasticity we discuss the dynamic boundary conditions taking into account surface stresses described by the Steigmann–Ogden model. The variational approach is applied with the use of the least action functional. The functional is represented as a sum of surface and volume integrals. The surface strain and kinetic energy densities are introduced. The Toupin–Mindlin formulation of the strain gradient elasticity...
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Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity
PublicationIn this paper we consider existence and uniqueness of the three-dimensional static boundary-value problems in the framework of so-called gradient-incomplete strain-gradient elasticity. We call the strain-gradient elasticity model gradient-incomplete such model where the considered strain energy density depends on displacements and only on some specific partial derivatives of displacements of first- and second-order. Such models...
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On nonlinear dilatational strain gradient elasticity
PublicationWe call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of placement. It is an interesting particular case of complete Toupin–Mindlin nonlinear strain gradient elasticity: indeed, in it, the...
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Justyna Płotka-Wasylka dr hab. inż.
PeopleUrodziła się w Słupsku (24.03.1986).W 2005 roku ukończyła I Liceum Ogólnokształcące im. Jana II Sobieskiego w Wejherowie i rozpoczęła studia na Wydziale Chemicznym Politechniki Gdańskiej. Po ich ukończeniu w 2010 rozpoczęła pracę naukową na tej uczelni, uzyskując w 2014 roku stopień doktora nauk chemicznych. Tematem jej rozprawy doktorskiej, wykonywanej pod kierunkiem prof. Marka Biziuka oraz dr Caluma Morrisona (Uniwersytet w...
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On the Equations of the Surface Elasticity Model Based on the Theory of Polymeric Brushes
PublicationMotivating by theory of polymers, in particular, by the models of polymeric brushes we present here the homogenized (continual) two-dimensional (2D) model of surface elasticity. A polymeric brush consists of an system of almost aligned rigid polymeric chains. The interaction between chain links are described through Stockmayer potential, which take into account also dipole-dipole interactions. The presented 2D model can be treated...
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Torsional elasticity and energetics of F1-ATPase
PublicationFoF1-ATPase is a rotary motor protein synthesizing ATP from ADP driven by a cross-membrane proton gradient. The proton flow through the membrane-embedded Fo generates the rotary torque that drives the rotation of the asymmetric shaft of F1. Mechanical energy of the rotating shaft is used by the F1 catalytic subunit to synthesize ATP. It was suggested that elastic power transmission with transient storage of energy in some compliant...
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Stress-driven nonlocal elasticity for nonlinear vibration characteristics of carbon/boron-nitride hetero-nanotube subject to magneto-thermal environment
PublicationStress-driven nonlocal theory of elasticity, in its differential form, is applied to investigate the nonlinear vibrational characteristics of a hetero-nanotube in magneto-thermal environment with the help of finite element method. In order to more precisely deal with the dynamic behavior of size-dependent nanotubes, a two-node beam element with six degrees-of freedom including the nodal values of the deflection, slope and curvature...
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Geometrically Nonlinear Analysis of Functionally Graded Shells Based on 2-D Cosserat Constitutive Model
PublicationIn this paper geometrically nonlinear analysis of functionally graded shells in 6-parameter shell theory is presented. It is assumed that the shell consists of two constituents: ceramic and metal. The mechanical properties are graded through the thickness and are described by power law distribution. Formulation based on 2-D Cosserat constitutive model is used to derive constitutive relation for functionally graded shells. Numerical...
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A Note on Reduced Strain Gradient Elasticity
PublicationWe discuss the particular class of strain-gradient elastic material models which we called the reduced or degenerated strain-gradient elasticity. For this class the strain energy density depends on functions which have different differential properties in different spatial directions. As an example of such media we consider the continual models of pantographic beam lattices and smectic and columnar liquid crystals.
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On weak solutions of boundary value problems within the surface elasticity of Nth order
PublicationA study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to Nth order. The virtual work principle, extended for higher‐order strain gradient media, serves as a basis for defining...
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Linear Micropolar Elasticity Analysis of Stresses in Bones Under Static Loads
PublicationWe discuss the finite element modeling of porous materials such as bones using the linear micropolar elasticity. In order to solve static boundary-value problems, we developed new finite elements, which capture the micropolar behavior of the material. Developed elements were implemented in the commercial software ABAQUS. The modeling of a femur bone with and without implant under various stages of healing is discussed in details
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Overview of the three multicriteria approaches applied to a global assessment of analytical methods
PublicationCritical and global evaluation of analytical methods should be one of the primary goals in analytical chemistry. A holistic approach, however, requires a look at the varied features: commonly discussed validation criteria, often underrated practical and economic aspects, and typically overlooked compliance with the principles of green analytical chemistry. Carrying out such an assessment in a critical and transparent way is extremely...
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ON DYNAMICS OF ELASTIC NETWORKS WITH RIGID JUNCTIONS WITHIN NONLINEAR MICRO-POLAR ELASTICITY
PublicationWithin the nonlinear micropolar elasticity we discuss effective dynamic (kinetic) properties of elastic networks with rigid joints. The model of a hyperelastic micropolar continuum is based on two constitutive relations, i.e., static and kinetic ones. They introduce a strain energy density and a kinetic energy density, respectively. Here we consider a three-dimensional elastic network made of three families of elastic fibers connected...
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Study on Methods to Control Interstory Deflections
PublicationOne of the possibilities to prevent building pounding between two adjacent structures is to consider appropriate in-between separation distance. Another approach might be focused on controlling the relative displacements during seismic excitations. Although the majority of building codes around the world recommend the use of some equations of various distances between structures to avoid pounding; a lot of reports after earthquakes...
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Application of shifted Chebyshev polynomial-based Rayleigh–Ritz method and Navier’s technique for vibration analysis of a functionally graded porous beam embedded in Kerr foundation
PublicationPresent study is dealt with the applicability of shifted Chebyshev polynomial based Rayleigh-Ritz method and Navier’s technique on free vibration of Functionally Graded (FG) beam with uniformly distributed porosity along the thickness of the beam. The material properties such as Young’s modulus, mass density, and Poisson’s ratio are also considered to vary along the thickness of the FG beam as per the power-law exponent model....
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On the correspondence between two- and three-dimensional Eshelby tensors
PublicationWe consider both three-dimensional (3D) and two-dimensional (2D) Eshelby tensors known also as energy–momentum tensors or chemical potential tensors, which are introduced within the nonlinear elasticity and the resultant nonlinear shell theory, respectively. We demonstrate that 2D Eshelby tensor is introduced earlier directly using 2D constitutive equations of nonlinear shells and can be derived also using the throughthe-thickness...
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Theory of Elasticity and Plasticity
e-Learning CoursesThis course discusses the general theory of elastic and plastic material behavior of solids.
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Strongly anisotropic surface elasticity and antiplane surface waves
PublicationWithin the new model of surface elasticity, the propagation of anti-plane surface waves is discussed. For the proposed model, the surface strain energy depends on surface stretching and on changing of curvature along a preferred direction. From the continuum mechanics point of view, the model describes finite deformations of an elastic solid with an elastic membrane attached on its boundary reinforced by a family of aligned elastic...
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Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory
PublicationThis article is intended to analyze forced vibrations of a piezoelectric-piezomagnetic ceramic nanoplate by a new refined shear deformation plate theory in conjunction with higher-order nonlocal strain gradient theory. As both stress nonlocality and strain gradient size-dependent effects are taken into account using the higher-order nonlocal strain gradient theory, the governing equations of the composite nanoplate are formulated....
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Non-linear static stability of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo-elasticity using nonlocal continuum
PublicationIn this research, the shear and thermal buckling of bi-layer rectangular orthotropic carbon nanosheets embedded on an elastic matrix using the nonlocal elasticity theory and non-linear strains of Von-Karman was studied. The bi-layer carbon sheets were modeled as a double-layered plate, and van der Waals forces between layers were considered. The governing equations and boundary conditions were obtained using the first order shear...
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Food Analytical Methods
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On Effective Bending Stiffness of a Laminate Nanoplate Considering Steigmann–Ogden Surface Elasticity
PublicationAs at the nanoscale the surface-to-volume ratio may be comparable with any characteristic length, while the material properties may essentially depend on surface/interface energy properties. In order to get effective material properties at the nanoscale, one can use various generalized models of continuum. In particular, within the framework of continuum mechanics, the surface elasticity is applied to the modelling of surface-related...
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On Anti-Plane Surface Waves Considering Highly Anisotropic Surface Elasticity Constitutive Relations
PublicationWithin the framework of highly anisotropic surface elasticity model we discuss the propagation of new type of surface waves that are anti-plane surface waves. By the highly anisotropic surface elasticity model we mean the model with a surface strain energy density which depends on incomplete set of second derivatives of displacements. From the physical point of view this model corresponds to a coating made of a family of parallel...
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Strong ellipticity within the Toupin–Mindlin first strain gradient elasticity theory
PublicationWe discuss the strong ellipticity (SE) condition within the Toupin–Mindlin first strain gradient elasticity theory. SE condition is closely related to certain material instabilities and describes mathematical properties of corresponding boundary-value problems. For isotropic solids, SE condition transforms into two inequalities in terms of five gradient-elastic moduli.
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Silica-templated three-dimensional graphene xerogels
PublicationMost porous carbons require the uniform pore size distribution therefore many approaches have been applied to template the carbon scaffolds and among them the use of silica particles is the easiest and the most effective. After discovering of graphene, the whole family of new carbon nanomaterials arose and one of the promising materials is graphene xerogel (GX) with a three-dimensional, highly porous structure. This monograph reviews...
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Ab initio elasticity of chalcopyrites
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Strong ellipticity conditions and infinitesimal stability within nonlinear strain gradient elasticity
PublicationWe discuss connections between the strong ellipticity condition and the infinitesimal instability within the nonlinear strain gradient elasticity. The strong ellipticity (SE) condition describes the property of equations of statics whereas the infinitesimal stability is introduced as the positive definiteness of the second variation of an energy functional. Here we establish few implications which simplify the further analysis...
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Theory of Elasticity and Plasticity 2023
e-Learning CoursesThis course discusses the general theory of elastic and plastic material behavior of solids.
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Theory of Elasticity and Plasticity 2024
e-Learning CoursesThis course discusses the general theory of elastic and plastic material behavior of solids.
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Theory of Elasticity and Plasticity - Civil Engineering, sem. I
e-Learning CoursesPreliminaries in Solid Body Mechanics focused on 2D and 3D engineering structures, in analytical approach
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Recent Achievements in Constitutive Equations of Laminates and Functionally Graded Structures Formulated in the Resultant Nonlinear Shell Theory
PublicationThe development of constitutive equations formulated in the resultant nonlinear shell theory is presented. The specific features of the present shell theory are drilling rotation naturally included in the formulation and asymmetric measures of strains and stress resultants. The special attention in the chapter is given to recent achievements: progressive failure analysis of laminated shells and elastoplastic constitutive relation...