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The constitutive model with a single damage parameter describing creep-damage behaviour of metals with respect to the different sensitivity of the damage process due to tension and compression is incorporated into the ANSYS ®nite element code by modifying the user de®ned creep material subroutine. The procedure is veri®ed by comparison with solutions for beams and rectangular plates in bending based on the Ritz method. Various numerical tests show the sensitivity of long-term predictions to the mesh sizes and element types available for the creep analysis of thinwalled structures. IntroductionEngineering structures operating at elevated temperatures such as fossil power plants, chemical plants, reactors, etc. are designed with respect to increased requirements of safety and assurance of long-term reliability. One of the main factors which must be considered in the long-term structural analysis is time-dependent material behaviour coupled with damage evolution (Roche et al., 1992). A powerful tool for the lifetime prediction is the continuum damage mechanics approach which is based on the formulation of constitutive and evolution equations for inelastic strains and material damage. Incorporating these material models into the ®nite element code predictions of time-dependent stress, strain and damage ®elds can be performed by numerical solution of nonlinear initialboundary value problems (e.g. . The ®rst problem arising by creep damage analysis is the formulation of a phenomenological material model that is able to describe the sensitivity of creep strain and damage rate to the stress level, stress state, temperature level, environmental effects, etc. Such a model must be able to extrapolate the experimental creep data usually available from uniaxial short-term creep tests and realised for narrow stress ranges to the in-service loading conditions in the real structure. The second problem can be related to the quality of the ®nite element predictions particularly by analysis of structures with complex shapes.The structural analysis of thinwalled components (pressure vessels, pipes, pipe bends, etc.) can be performed using the mechanical models of plane stress (strain) states or equations of shell theory. In the case of plane stress (strain) problems numerous ®nite element simulations considering creep damage effects has been made because of experimental data available for veri®ca-tion. Examples are discussed by Saanouni et al. Since these examples con®rm the ability of ®nite element simulations to predict stress redistributions and failure times with accuracy enough for engineering applications and can be used as benchmark tests by development of user de®ned material subroutines incorporating damage evolution a little effort has been made for the analysis of transversely loaded thinwalled structures. Numerical results for rupture times of rectangular plates in bending are given by Bodnar and Chrzanowski (1994), Bialkiewicz and Mika (1995) based on in-house ®nite element codes and Altenbach and Naumenko (1997) for re...

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We present a method for solving problems of high-temperature cyclic creep and damage accumulation in structural elements. The asymptotic expansion and averaging techniques both over the period of forced vibrations of a body and that of slowly varying loads are used for the set of equations describing the creep and damage processes in thin-walled structural elements.Introduction. Structural elements of up-to-date equipment operating at elevated temperatures and under the combined action of both static and slowly or rapidly varying cyclic stresses are characterized by the processes of evolution of irreversible creep deformations and accumulation of concealed damage. Many of such elements correspond to calculation schemes for thin shells of revolution. Due to a wide use of thin-walled shells of revolution in aerospace, aircraft and power engineering, the questions arise as to simulation of their stress-strain states (SSS) under cyclic loading conditions [1].Most of the computational studies on the creep and fracture of shell structures were carried out only for the case of static loads. A number of works dealing with the evaluation of the influence of cyclic loading on the creep and long-term strength characteristics of plates and shells were published recently [2,3]. Under actual operating conditions of structural elements, their loading is a complex process -a combination of temperature and load cycles with greatly different periods. In this connection, the development of the method for solving problems of cyclic creep and damage accumulation is of importance. This paper presents the developed method as applied to thin-walled structures consisting of shells of revolution.Problem Statement and Solution Method. The formulated problems are solved using the finite element method (FEM). A finite element is used as a conical shell. According to the FEM approach, we write down the basic variational equality [2, 3] − − + =