Effective constants of piezoactive composites of stochastic structure (original) (raw)
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A three-dimensional asymptotic scheme that combines the transfer matrix method and the asymptotic expansion technique is used to analyze thermo-electro-mechanical deformations of a piezothermoelastic laminate with surface tractions, electric potentials, and temperatures specified on its top and bottom surfaces. The scheme results in a hierarchy of two-dimensional equations with the same homogeneous operator for each order.
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IOP Conference Series: Materials Science and Engineering
A theory of thin multilayer anisotropic viscoelastic cylindrical shells with allowance for quasistatic oscillations, based on the application of asymptotic analysis of small geometric parameters to the general three-dimensional equations of the viscoelasticity theory for curvilinear coordinates, is proposed. Recurrent sequences of local problems of the viscoelasticity theory for shells under the quasistatic pressure oscillations are formulated and analytical solutions are obtained. It is shown that with this approach it is possible to obtain expressions for all 6 components of the stress tensor over the thickness of the shell. An example of the calculation of a cylindrical viscoelastic shell with axisymmetric bending with allowance for quasistatic oscillations is considered. The graphs of the dependences of the components of the stress tensor on the local coordinate are given for different angles of layers in the material. An algorithm is proposed for obtaining explicit analytical equations for calculating the distribution of the total stress tensor components over a cylindrical shell under the action of quasistatic oscillations.
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A developed system is presented for computer aided calculation of the effective elastic properties of composite materials (CM) with various reinforcement structure (3D reinforced, 4D reinforced, textile reinforcement). The computation was based on the finite element method for the solution of the so called local problems L pq arising on applying the asymptotic homogenization method worked out by N.S. Bakhvalov and B.Ye. Pobedrya. The calculation results for effective elastic properties of CM obtained by the developed software system are presented as well as some character istics of the system application to the above listed types of reinforcement structures. CM (composites), which have been intensively developed since the 1960s, are still one of the leading classes of engineering materials due to their outstanding properties, i.e., low weight (even in comparison with aluminum alloys), high stiffness and strength, as well as their high chemical resistance, machinability, etc. The greatest disadvantage of these materials is their high price, which had earlier limited the scope of its application in civil engineering, but it has largely been overcome, since the price of the end product (e.g., aircraft or sea vessels) is now much less dependent on the prices of components and materials.
A multicontinuum theory for structural analysis of composite material systems
Composites Engineering, 1995
The success of modern continuum mechanics in modelling problems in solid mechanics is truly remarkable. For instance, the general theories of elasticity, plasticity, and viscoeleasticity all rely on the continuum hypothesis. However, while continuum mechanics has provided a powerful means of studying the physics of deformation of composite materials, there are situations when the continuum hypothesis is simply inadequate. These problems are generally associated with inelastic behavior and are mainly attributed to the necessity to homogenize two distinctly different materials into a single continuum. In this paper, we introduce a multicontinuum theory designed specifically for the analysis of composite material systems. The chief attribute of the theory is its ability to do structural analysis while allowing each constituent to retain its own identity. Major analytical and numerical advances in the theory originally developed by Hansen et al. [Hansen, A. C., Walker, J. L. and Donovan, R. P. (1994). A finite element formulation for composite structures based on a volume fraction mixture theory. ht. J. Engng Sci. 32, I-17.1 are presented. The utility of the theory is demonstrated by using constituent information to predict the yield surface of a unidirectional boron/aluminum composite in the course of an analysis carried out at the structural level. NOMENCLATURE Both direct tensor notation and contracted matrix notation are employed in this article. In direct notation, vectors are denoted by boldface characters, while second order tensors are underscored with a tilde. Fourth order tensors are both bold and underscored with a tilde. Microstructure tensor Contracted matrix form of the microstructure tensor Body force density for constituent (Y Composite material stiffness matrix Material matrix for constituent cy Young's modulus Uniform strain field applied to a unit cell. _ Shear modulus Unit normal to a surface Momentum supply for constituent cy Spatial domain Boundary of spatial domain R Stress traction Stress traction for constituent 01 Partial stress tensor for constituent o(Displacement for constituent (Y Volume Position vector Gradient operator Strain tensor for the composite Strain tensor for constituent cy Poisson's ratio Poisson's ratio for constituent (Y Dispersed density for constituent LY Volume fraction for constituent 01 Stress tensor for the composite Stress tensor for constituent 01 Uniform stress field applied to a unit cell Shear yield stress Subscripts p* Arbitrary constituent Arbitrary constituent m Composite material matrix constituent r Composite material reinforcement constituent 'On educational leave from Battelle-Pacific Northwest Laboratories.
Computers & Structures, 2006
In this paper a coupled Euler-Bernoulli model of laminated piezoelectric beams is proposed. It is characterized by accounting for the influence of 3D distribution of mechanical stresses and strains through corrected electromechanical constitutive equations. In particular, the hypothesis of vanishing transverse (width direction) normal stress typical of standard beam models is weakened by imposing vanishing stress resultants. This integral condition is enforced by adopting a mixed variational principle and Lagrange multiplier method. Explicit expressions for the beam constitutive coefficients are given and the sandwich and bimorph piezoelectric benders are studied in details. The model is assessed through comparisons with standard models and 3D finite element results, showing an important enhancement of standard beam theories. Here and henceforth the term dynamic is used in its etymological sense (e.g. related to force, power) to indicate the state variables which expend power on the kinematic fields. 2 S = sym(5u) on B and u = u 0 on o u B; E = À5u on B and u = u 0 on o u B.