Differential-algebraic approach to large deformation analysis of frame structures subjected to dynamic loads

A nonlinear mathematical model for the analysis of large deformation of frame structures with discontinuity conditions and initial displacements, subject to dynamic loads is formulated with arc-coordinates. The differential quadrature element method （DQEM） is then applied to discretize the nonlinear mathematical model in the spatial domain, An effective method is presented to deal with discontinuity conditions of multivariables in the application of DQEM. A set of DQEM discretization equations are obtained, which are a set of nonlinear differential-algebraic equations with singularity in the time domain. This paper also presents a method to solve nonlinear differential-algebra equations. As application, static and dynamical analyses of large deformation of frames and combined frame structures, subjected to concentrated and distributed forces, are presented. The obtained results are compared with those in the literatures. Numerical results show that the proposed method is general, and effective in dealing with disconti- nuity conditions of multi-variables and solving differential-algebraic equations. It requires only a small number of nodes and has low computation complexity with high precision and a good convergence property.     

Numerical-analytical solution of plane problems in thermoelasticity

The scaled-boundary method is used as a numerical-analytical method to solve problems of thermoelasticity. As an example, the stress intensity factor for a heated thin circular orthotropic disk with an internal crack is evaluated __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 122–126, December 2007.     

A boundary element method for anisotropic coupled thermoelasticity

Summary A boundary element formulation is presented for the solution of the equations of fully coupled thermoelasticity for materials of arbitrary degree of anisotropy. By employing the fundamental solutions of anisotropic elastostatics and stationary heat conduction, a system of equations with time-independent matrices is obtained. Since the fundamental solutions are uncoupled and time-independent, a domain integral remains in the representation formula which contains the time-dependence as well as the thermoelastic coupling. This domain integral is transformed to the boundary by means of the dual reciprocity method. By taking this approach, the use of dynamic fundamental solutions is avoided, which enables an efficient calculation of system matrices. In addition, the solution of transient processes as well as, free and forced vibration analysis becomes straightforward and can be carried out with standard time-stepping schemes and eigensystem solvers. Another important advantage of the present formulation is its versatility, since it includes a number of simplified thermoelastic theories, viz. the theory of thermal stresses, coupled and uncoupled quasi-static thermoelasticity, and stationary thermoelasticity. The accuracy of the new thermoelastic boundary element method is demonstrated by a number of example problems. Support by the Deutsche Forschungsgemeinschaft (DFG) of the Graduate Collegium Modelling and discretization methods for continua and fluids (GKKS) at the University of Stuttgart is gratefully acknowledged.     

State-space approach to two-temperature generalized thermoelasticity without energy dissipation of medium subjected to moving heat source

In this work,a model of two-temperature generalized thermoelasticity without energy dissipation for an elastic half-space with constant elastic parameters is constructed.The Laplace transform and state-space techniques are used to obtain the general solution for any set of boundary conditions.The general solutions are applied to a specific problem of a half-space subjected to a moving heat source with a constant velocity.The inverse Laplace transforms are computed numerically,and the comparisons are shown in figures to estimate the effects of the heat source velocity and the two-temperature parameter.     

Closed solutions of boundary-value problems of coupled thermoelasticity

Coupled equations of thermoelasticity take into account the effect of nonuniform heating on the medium deformation and that of the dilatation rate on the temperature distribution. As a rule, the coupling coefficients are small and it is assumed, sometimes without proper justification, that the effect of the dilatation rate on the heat conduction process can be neglected. The aim of the present paper is to construct analytical solutions of some model boundary-value problems for a thermoelastic bounded body and to determine the body characteristic dimensions and the medium thermomechanical moduli forwhich it is necessary to take into account that the temperature and displacement fields are coupled. We consider some models constructed on the basis of the Fourier heat conduction law and the generalized Cattaneo-Jeffreys law in which the heat flux inertia is taken into account. The solution is constructed as an expansion in a biorthogonal system of eigenfunctions of the nonself-adjoint operator pencil generated by the coupled equations of motion and heat conduction. For the model problem, we choose a special class of boundary conditions that allows us to exactly determine the pencil eigenvalues.     

State-space approach of two-temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading

In this work, we will consider an infinite elastic body with a spherical cavity and constant elastic parameters. The governing equations are taken in the context of the two-temperature generalized thermoelasticity theory (Youssef in J Appl Math Mech 26(4):470–475 2005a, IMA J Appl Math, pp 1–8, 2005). The medium is assumed initially quiescent. Laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem when the bounding plane of the cavity is subjected to thermal loading (thermal shock and ramp-type heating). The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the two-temperature and the ramping parameters.     

Multi-scale FE computation for the structures of composite materials with small periodic configuration under condition of coupled thermoelasticity

In this paper, the multi-scale computational method for a structure of composite materials with a small periodic configuration under the coupled thermoelasticity condition is presented. The two-scale asymptotic (TSA) expression of the displacement and the increment of temperature for composite materials with a small periodic configuration under the condition of thermoelasticity are briefly shown at first, then the multi-scale finite element algorithms based on TSA are discussed. Finally the numerical results evaluated by the multi-scale computational method are shown. It demonstrates that the basic configuration and the increment of temperature strongly influence the local strains and local stresses inside a basic cell. The project supported by the National Natural Science Foundation of China (19932030) and Special Funds for Major State Basic Research Projects     

RESTUDY OF COUPLED FIELD THEORIES FOR MICROPOLAR CONTINUA (Ⅰ)──MICROPOLAR THERMOELASTICITY

ＩｎｔｒｏｄｕｃｔｉｏｎＳｏｍｅａｕｔｈｏｒｓｓｔｕｄｉｅｄｔｈｅｃｏｕｐｌｅｄｆｉｅｌｄｐｒｏｂｌｅｍｓｆｏｒｍｉｃｒｏｐｏｌａｒｃｏｎｔｉｎｕａ .Ｅｓｐｅｃｉａｌｌｙ ,Ｗ .Ｎｏｗａｃｋｉｐｕｂｌｉｓｈｅｄａｓｅｒｉｅｓｏｆａｂｏｕｔ 4 0ｓｃｉｅｎｔｉｆｉｃｐａｐｅｒｓｄｅａｌｉｎｇｗｉｔｈｔｈｅｍｉｃｒｏｐｏｌａｒｔｈｅｒｍｏｅｌａｓｔｉｃｉｔｙａｓｗｅｌｌａｓｔｈｅｐｒｏｂｌｅｍｓｏｆｄｉｓｔｏｒｔｉｏｎ ,ｔｈｅｒｍｏｄｉｆｆｕｓｉｏｎ ,ｔｈｅｒｍｏｐｉｅｚｏｅｌｅｃｔｒｉｃｉｔｙａｎｄｍ…     

Analytical solutions to the 2D elasticity and thermoelasticity problems for inhomogeneous planes and half-planes

This paper presents a method for analytical solving the plane elasticity and thermoelasticity problems for planes and half-planes which exhibit inhomogeneous material properties in one of the planar directions (in the case of half-plane, the inhomogeneity direction is assumed to be perpendicular to the boundary.) With the aid of direct integration of equilibrium equations, the original problems are reduced to the set of governing, harmonic equations with corresponding conditions. In the transform domain of the integral Fourier-transform, the governing equations are reduced to an integral equation which is solved by simple iteration technique. The rapid convergence of the iterative procedure is established to perform the numerical calculation. The authors gratefully acknowledge the financial support of this research by the National Science Council (Republic of China) under Grant NSC 95-2221-E-002-048-MY2. The co-author, Yu Tokovyy, gratefully acknowledges the particular financial support of this research by the grant of the President of Ukraine for young scientists (No GP/F13/0094).     

A variational principle for the dynamic problem of linear coupled thermoelasticity

Summary A functional is constructed by whose stationarity the mixed problem for linear and dynamic thermoelasticity is obtained. In contrast with previous results[2], [4], [8], neither constrained variations nor previous transformations upon the equations of the problem are used. The unrestricted variational formulation is made possible by means of a convolutive bilinear form.

---

Sommario Si costruisce un funzionale dalla cui stazionarietà si ricava il problema misto della termoelasticità lineare accoppiata. A differenza di precedenti risultati[2], [4], [8] non si ricorre né a variazioni bloccate né a preliminari trasformazioni del problema. La formulazione variazionale non ristretta è resa possibile dall'uso di una forma bilineare convolutiva.

---

---

Work done in the sphere of activity of the Group for Mathematical Research of the (Italian) C.N.R.     

A generalized variational principle in micromorphic thermoelasticity

Recently Nappa obtains a Gurtin-type variational principle for micromorphic thermoelasticity. However, the use of convolutions is of course restricted to the linear case, which sets a limit to the rang of applicability. This paper establishes a classic variational principles for the discussed problem by the semi-inverse method.     

Homogenization in finite thermoelasticity

A homogenization framework is developed for the finite thermoelasticity analysis of heterogeneous media. The approach is based on the appropriate identifications of the macroscopic density, internal energy, entropy and thermal dissipation. Thermodynamical consistency that ensures standard thermoelasticity relationships among various macroscopic quantities is enforced through the explicit enforcement of the macroscopic temperature for all evaluations of temperature dependent microscale functionals. This enforcement induces a theoretical split of the accompanying micromechanical boundary value problem into two phases where a mechanical phase imposes the macroscopic deformation and temperature on a test sample while a subsequent purely thermal phase on the resulting deformed configuration imposes the macroscopic temperature gradient. In addition to consistently recovering standard scale transition criteria within this framework, a supplementary dissipation criterion is proposed based on alternative identifications for the macroscopic temperature gradient and heat flux. In order to complete the macroscale implementation of the overall homogenization methodology, methods of determining the constitutive tangents associated with the primary macroscopic variables are discussed. Aspects of the developed framework are demonstrated by numerical investigations on model microstructures.     

Problem of coupled thermoelasticity for a half-layer with a tunnel cavity: An antisymmetric case

A boundary-value problem of coupled thermoelasticity for a half-layer with a hole and mixed boundary conditions is solved. The problem is reduced to a system of four singular integral equations. It is solved numerically using the mechanical-quadrature method. A numerical experiment is conducted to study the dynamic stress concentration around cavities of different cross sections. The effect of the coupled thermal and elastic fields on the wave processes in the body is established Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 28–36, October 2008.     

Evolutionary model of finite-strain thermoelasticity

The equation of state of finite-strain thermoelasticity is obtained using a formalized approach to constructing constitutive relations for complex media under the assumption of closeness of intermediate and current configurations. A variational formulation of the coupled thermoelastic problem is proposed. The constitutive equation, the heat-conduction equation, the relations for internal energy, free energy, and entropy, and the variational formulation of the coupled problem of finite-strain thermoelasticity are tested on the problem of uniaxial extension of a bar. The model adequately describes experimental data for elastomers, such as entropic elasticity, temperature inversion, and temperature variation during an adiabatic process. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 184–196, May–June, 2008.     

Coupled thermoelasticity of functionally graded cylindrical shells

The coupled thermoelastic response of a functionally graded circular cylindrical shell is studied. The coupled thermoelastic and the energy equations are simultaneously solved for a functionally graded axisymmetric cylindrical shell subjected to thermal shock load. A second-order shear deformation shell theory that accounts for the transverse shear strains and rotations is considered. Including the thermo-mechanical coupling and rotary inertia, a Galerkin finite element formulation in space domain and the Laplace transform in time domain are used to formulate the problem. The inverse Laplace transform is obtained using a numerical algorithm. The shell is graded through the thickness assuming a volume fraction of metal and ceramic, using a power law distribution. The results are validated with the known data in the literature.