Multi thermal waves in a thermo diffusive piezo electric functionally graded rod via refined multi-dual phase-lag model

none5siIn the present work, a novel analytical modelis provided for wave dispersion in a piezo-thermoelasticdiffusive functionally graded rod through the multi-phaselag model and thermal activation. The plain strain modelfor thermo piezoelectric functionally graded rod is consid-ered. The complex characteristic equations are obtained byusing normal mode method which satisfies the nonlinearboundary conditions of piezo-thermoelastic functionallygraded rod. The numerical calculations are carried out forcopper material. The results of the variants stress, mechan-ical displacement, temperature and electric distribution,frequency are explored against the geometric parametersand some special parameters graded index, concentrationconstants are shown graphically. The observed results willbe discuss elaborate. The results can be build reasonableattention in piezo-thermoelastic materials and smart mate-rials industry.Jeyaraman P.; Mahesh S.; Selvamani R.; Dimitri R.; Tornabene F.Jeyaraman, P.; Mahesh, S.; Selvamani, R.; Dimitri, R.; Tornabene, F

Solution of Coupled Thermoelasticity Problem in Rotating Disks

The main purpose of this dissertation is to study coupled thermoelastic behaviors in disks subjected to thermal shock loads based on the generalized and classic theories of coupled thermoelasticity. To this end, this research has been carried out in two stages. In the first stage, thermoelasticity problems in an axisymmetric rotating disk with constant thickness made of a homogeneous isotropic material are analytically solved and closed-form formulations are presented for temperature and displacement fields. Since, the analytical solution is not always feasible, the finite element (FE) method can be employed for more sophisticated coupled thermoelasticity problems. Accordingly, in the second stage of the research, a novel refined 1D finite element approach with 3D-like accuracies are developed for theories of coupled thermoelasticity. Then, the developed FE models are applied for a 3D solution of the dynamic generalized coupled thermoelasticity problem in disks. Use of the reduced models with low computational costs may be of interest in a laborious time history analysis of the dynamic problems. The obtained analytical and numerical solutions are in good agreement with the results available in the literature. It is further shown that the proposed analytical and FE methods are quite efficient with very high rate of convergence

A New Boundary Element Formulation for Modeling and Optimization of Three-Temperature Nonlinear Generalized Magneto-Thermoelastic Problems of FGA Composite Microstructures

The main purpose of this chapter is to propose a new boundary element formulation for the modeling and optimization of three-temperature nonlinear generalized magneto-thermoelastic functionally graded anisotropic (FGA) composite microstructures’ problems, which is the gap of this study. Numerical results show that anisotropy and the functionally graded material have great influences on the nonlinear displacement sensitivities and nonlinear thermal stress sensitivities of composite microstructure optimization problem. Since, there are no available data for comparison, except for the problems with one-temperature heat conduction model, we considered the special case of our general study based on replacing three-temperature radiative heat conductions with one-temperature heat conduction. In the considered special case, numerical results demonstrate the validity and accuracy of the proposed technique. In order to solve the optimization problem, the method of moving asymptotes (MMA) based on the bi-evolutionary structural optimization method (BESO) has been implemented. A new class of composite microstructures problems with holes or inclusions was studied. The two-phase magneto-thermoelastic composite microstructure which is studied in this chapter consists of two different FGA materials. Through this chapter, we investigated that the optimal material distribution of the composite microstructures depends strongly on the heat conduction model, functionally graded parameter, and shapes of holes or inclusions

Axisymmetric Thermoelastic Response in a Semi-elliptic Plate With Kassir’s Nonhomogeneity in the Thickness Direction

The main objective is to investigate the transient thermoelastic reaction in a nonhomogeneous semi-elliptical elastic plate heated sectionally on the upper side of the semi-elliptic region. It has been assumed that the thermal conductivity, calorific capacity, elastic modulus and thermal coefficient of expansion were varying through thickness of the nonhomogeneous material according to Kassir’s nonhomogeneity relationship. The transient heat conduction differential equation is solved using an integral transformation technique in terms of Mathieu functions. In these formulations, modified total strain energy is obtained by incorporating the resulting moment and force within the energy term, thus reducing the step of the calculation. The thermal deflection equation derived from the Berger approach is compared with Von Karman approaches, and its maximum normal stresses are determined. The numerical calculation is performed over the metal-metal based composite and graphically portrayed. Furthermore, by applying limiting conditions, the semi-elliptic region can be degenerate into a semi-circular plate. Results reveal that the highest tensile stress exists on the semi-circular core relative to the semi-elliptical core, suggesting the propagation of low heating due to insufficient heat penetration into the elliptic surface

Some new thermo-elastic solutions for cylindrical and spherical composites

In modern engineering applications, multilayered structures are extensively used due to the added advantage of combining physical, mechanical, and thermal properties of different materials. Many of these applications require a detailed knowledge of transient temperature and heat-flux distribution within the component layers. Both analytical and numerical techniques may be used to solve such problems. Nonetheless, numerical solutions are preferred and prevalent in practice, due to either unavailability or higher mathematical complexity of the corresponding exact solutions. Rather limited use of analytical solutions should not diminish their merit over numerical ones; since exact solutions, if available, provide an insight into the governing physics of the problem, which is typically missing in any numerical solution. Moreover, analyzing closed-form solutions to obtain optimal design options for any particular application of interest is relatively simpler. In addition, exact solutions find their applications in validating and comparing various numerical algorithms to help improve computational efficiency of computer codes that currently rely on numerical techniques. Although multilayer heat conduction problems have been studied in great detail and various solution methods including orthogonal and quasi-orthogonal expansion technique, Laplace transform method, Green’s function approach, finite integral transform technique are readily available; there is a continued need to develop and explore novel methods to solve problems for which exact solutions still do not exist. One such problem is to determine exact unsteady temperature distribution in polar coordinates with multiple layers in the radial direction. Numerous applications involving multilayer cylindrical geometry require evaluation of temperature distribution in complete disk-type. One typical example is a nuclear fuel rod, which consists of concentric layers of different materials and often subjected to asymmetric boundary conditions. Moreover, several other applications including multilayer insulation materials, double heat-flux conductimeter, typical laser absorption calorimetry experiments, cryogenic systems, and other cylindrical building structures would benefit from such analytical solutions. Then, object of the present thesis is to derive new thermo-elastic solutions for composite materials constituted by multilayered spheres and cylinders under time-dependent boundary conditions. These solutions are utilized for several engineering applications and we report some applications in last analyze chapters of present thesis. In follows, we will described the contents of thesis. In first chapters are reported the thermo-mechanical foundations and a summary of the formulation of thermo-elastic problems for isotropic material. In chapter X it is developed an analytical approach to find exact elastic solutions for multilayered cylinder composed of isotropic constituents and determining the analytical response in terms of displacements and stresses for all the De Saint Venant (DSV) load conditions, that is axial force, torque, pure bending and combined bending moment and shear actions. Successively, on the basis of the found analytical solutions, a homogenization procedure is adopted in order to obtain the overall constitutive elastic laws for multilayered cylinder, in this way deriving the exact one-dimensional model characterized by the axial stiffness, flexural rigidity, shear deformability and torsional stiffness relating beam’s generalized stresses and strains. By playing with the Poisson ratios of adjacent phases, some counterintuitive and engineering relevant results are shown with reference to unexpected increasing of overall stiffness of multilayered cylinder. In chapter XI it is presented an analytical elastic solution for multilayered cylinder constituted by transversally-isotropic n-phases, under radial pressure, axial force and torque. Then, by utilizing the homogenization theory, it is obtained the overall elastic stiffness of the equivalent homogeneous transversally-isotropic solid, establishing the constitutive elastic laws relating stresses and strains. In chapter XII it is developed an analytical approach to find exact elastic solutions for multilayered cylinder subjected to axial force, constituted by n orthotropic cylindrical hollow phases and a central core, each of them modelled as homogeneous and cylindrically anisotropic material. In chapter XIII it is reported an analytical solution for multilayered cylinder composed by hollow cylindrical monoclinic phases under axial force and torsion. In this chapter, we consider the chiral structure for each cylindrical layer. In particular the composite material is constituted by two hollow cylindrical monoclinic phases. The cylindrical monoclinic elastic property of multilayered cylinder is obtained by the particular chiral structure. In fact, we consider the two hollow phases constructed by right-handed and left-handed spiral helices whose long axes are all parallel. These helical spirals may be either touching or separated by a matrix material and are composed by elastic orthotropic material. In chapters XIV, XV, XVI are reported some thermo-elastic solution, for hollow cylinders, hollow spheres and plates, respectively. In chapter XVII we consider a steady-state thermo-elastic problem of multilayered cylinder with finite length. The thermal and mechanical loads applied on the cylinder are axisymmetric in the hoop direction and are constant in the axial direction. In order to obtain analytical solutions for temperature, displacements, and stresses for the two-dimensional thermo-elastic problem, the cylinder is assumed to be composed of n fictitious layers in the radial direction. The material properties of each layer are assumed as homogeneous. In chapter XVIII are determined the displacements, strains, and stresses from the general analytical solution of multilayered sphere composed by an arbitrary number of layers constituted by materials with generic modulus of elasticity, thermal expansion coefficient and thermal conductivity. Material properties are assumed to be temperature-independent and homogeneous in each layer. The multilayered sphere is considered as a classical composite material whose properties abruptly vary from one hollow sphere to the other. In chapter XIX are presented the most important standard fire curves: ISO 834, External fire curve, hydrocarbon fire curve, ASM119 and parametric fire curves (European Parametric fire curves, Swedish Fire Curves, BFD curves, CE 534 curve). Moreover in this chapter are reported the mechanical and thermal properties of steel and concrete at elevate temperature. In chapters XX and XXI, the one-dimensional quasi-static uncoupled thermo-elastic problem of a multilayered sphere and multilayered cylinder, with time-dependent boundary conditions are considered, respectively. The body forces and heat generation vanish. In both cases, the analytical solution is obtained by applying the method of separation of variables. In chapter XXII it is studied a spherical tank methane gas-filled exposed to fire characterized by hydrocarbon fire curve. The interaction between spherical tank and internal gas is studied. By applying a suitable simplified hypothesis on the mechanics of problem, we determine the analytical thermo-elastic solution for spherical tank. By applying the solution obtained, the increasing graded temperature of gas methane in spherical tank is determined. Finally, a numerical example is reported for a spherical tank exposed to hydrocarbon fire, showing the collapse temperature. In chapter XXIII, an industrial insulated pipeline is modelled as multilayered cylinder, subjected to mechanical and thermal loads. By using a multi-layered approach based on the theory of laminated composites, the solutions for temperature, heat flux, displacements, and thermal/mechanical stresses are presented. By applying the analytical thermo-elastic solution reported in Chapter XVII, a parametric analysis is conducted in order to analyze the mechanical behaviour of an industrial insulated pipeline composed by three phases: steel, insulate coating, and outer layer made of polyethylene to protect the insulation. In this model, parametric analyses are conducted by varying the Young’s modulus, Poisson’s ratio, thermal conductivity and linear thermal expansion coefficient of insulate coating. The analysis shows the maximum Hencky von Mises’s equivalent stress in steel phase and in insulate coating. Finally, it is presented a numerical example by considering three types of materials for insulate coating: (1) Expanded Polyurethane; (2) Laminate glass; (3) Syntatic foam. In chapter XXIV it is analyzed a cylindrical concrete specimen under axial force within Fibre Polymeric Reinforcing sheets. The elastic solutions found in Chapter XII are here extended to the post-elastic range. The evolution of the stress field when the core phase is characterized by an Intrinsic Curve or Schleicher-like elastic-plastic response with associate flow rule and the cylindrically orthotropic hollow phase obeys to is shown the elastic-brittle Tsai-Hill anisotropic yield criterion. The choice of these post-elastic behaviours is suggested by experimental evidences reported in literature for these materials, as well as the cylindrical orthotropy of the hollow phase intrinsically yields to consider several perfectly bonded FRP layers as an equivalent one, interpreting their overall mechanical response by invoking the theory of homogenization and the mechanics of composites. At the end, a numerical example application to cylindrical concrete specimens reinforced with Carbon FRP is presented, by furnishing a predictive formula – derived from the previously obtained analytical solutions - for estimating the overall collapse mechanism, the concrete ultimate compressive strength and the confining pressure effect. The results are finally compared with several experimental literature data, highlighting the very good agreement between the theoretical predictions and the laboratory measurements. In chapter XXV it is reported an analytical thermo-elastic solution in closed form for bi-layer hollow cylinder subjected to time-dependent boundary conditions. It is assumed that each hollow cylinder is composed by a homogeneous and thermo-isotropic material, characterized by different mechanical and thermal parameters, i.e. modulus of elasticity, thermal expansion coefficient and thermal conductivity. Moreover, these material properties in each hollow cylinder are assumed to be temperature-independent. In other words, the bi-layer hollow cylinder is considered as a classical composite material whose properties abruptly vary from one hollow cylinder to the other. In particular, it is obtained a new analytical solution for a bi-layer hollow cylinder, constituted by two phases: Ceramic ( ) and Metal ( ) subjected to heat flux on inner surface

A variational framework for mathematically nonsmooth problems in solid and structure mechanics

This dissertation presents a new paradigm for addressing multi-physics problems with interfaces in the field of Additive Manufacturing and the modeling of fibrous composite materials. The unique process of adding the material layer by layer in the AM techniques raises the issue about the stability of the interfaces between the layers and along the boundaries of multi-constituent materials. A stabilized interface formulation is developed to model debonding in monotonic loading, fatigue effects in cyclic loading, and thermal effects at interfaces which severely impact the functional life of those materials and structures. The formulation is based on embedding Discontinuous Galkerin (DG) ideas in a Continuous Galerkin (CG) framework. Starting from a mixed method incorporating the Lagrange multiplier along the interface, a pure displacement formulation is derived using the Variational Multiscale Method (VMS). From a mathematical and computational perspective, the key factor influencing the accuracy and robustness of the interface formulation is the design of the numerical flux and the penalty or stability terms. Analytical expressions that are free from user-defined parameters are naturally derived for the numerical flux and stability tensor which are functions of the evolving geometric and material nonlinearity. The proposed framework is extended for debonding at finite strains across general bimaterial interfaces. An interfacial gap function is introduced that evolves subject to constraints imposed by opening and/or sliding interfaces. An internal variable formalism is derived together with the notion of irreversibility of damage results in a set of evolution equations for the gap function that seamlessly tracks interface debonding by treating damage and friction in a unified way. Tension debonding, compression damage, and frictional sliding are accommodated, and return mapping algorithms in the presence of evolving strong discontinuities are developed. This derivation variationally embeds the interfacial kinematic models that are crucial to capturing the physical and mathematical properties involving large strains and damage. The framework is extended for monolithic coupling of thermomechanical fields in the class of problems that have embedded weak and strong discontinuities in the mechanical and thermal fields. Since the derived expressions are a function of the mechanical and thermal fields, the resulting stabilized formulation contains numerical flux and stability tensors that provide an avenue to variationally embed interfacial kinetic and kinematic models for more robust representation of interfacial physics. Representative numerical tests involving large strains and rotations, damage phenomena, and thermal effects are performed to confirm the robustness and accuracy of the method. Comparison of the results with both experimental and numerical results from literature are presented.Ope

Applicable Solutions in Non-Linear Dynamical Systems

From Preface: The 15th International Conference „Dynamical Systems - Theory and Applications” (DSTA 2019, 2-5 December, 2019, Lodz, Poland) gathered a numerous group of outstanding scientists and engineers who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without great effort of the staff of the Department of Automation, Biomechanics and Mechatronics of the Lodz University of Technology. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our event was attended by over 180 researchers from 35 countries all over the world, who decided to share the results of their research and experience in different fields related to dynamical systems. This year, the DSTA Conference Proceedings were split into two volumes entitled „Theoretical Approaches in Non-Linear Dynamical Systems” and „Applicable Solutions in Non-Linear Dynamical Systems”. In addition, DSTA 2019 resulted in three volumes of Springer Proceedings in Mathematics and Statistics entitled „Control and Stability of Dynamical Systems”, „Mathematical and Numerical Approaches in Dynamical Systems” and „Dynamical Systems in Mechatronics and Life Sciences”. Also, many outstanding papers will be recommended to special issues of renowned scientific journals.Cover design: Kaźmierczak, MarekTechnical editor: Kaźmierczak, Mare

Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Multibody Systems with Flexible Elements

Multibody systems with flexible elements represent mechanical systems composed of many elastic (and rigid) interconnected bodies meeting a functional, technical, or biological assembly. The displacement of each or some of the elements of the system is generally large and cannot be neglected in mechanical modeling. The study of these multibody systems covers many industrial fields, but also has applications in medicine, sports, and art. The systematic treatment of the dynamic behavior of interconnected bodies has led to an important number of formalisms for multibody systems within mechanics. At present, this formalism is used in large engineering fields, especially robotics and vehicle dynamics. The formalism of multibody systems offers a means of algorithmic analysis, assisted by computers, and a means of simulating and optimizing an arbitrary movement of a possibly high number of elastic bodies in the connection. The domain where researchers apply these methods are robotics, simulations of the dynamics of vehicles, biomechanics, aerospace engineering (helicopters and the behavior of cars in a gravitational field), internal combustion engines, gearboxes, transmissions, mechanisms, the cellulose industry, simulation of particle behavior (granulated particles and molecules), dynamic simulation, military applications, computer games, medicine, and rehabilitation