The Effect of Structural Curvings on the Stress Distribution in a Rigidly Fixed Composite Plate under Forced Vibration

Based on the exact three-dimensional equations of continuum mechanics and the Akbarov-Guz' continuum theory, the problem on forced vibrations of a rectangular plate made of a composite material with a periodically curved structure is formulated. The plate is rigidly fixed along the Ox ₁ axis. Using the semi-analytic method of finite elements, a numerical procedure is elaborated for investigating this problem. The numerical results on the effect of structural curvings on the stress distribution in the plate under forced vibrations are analyzed. It is shown that the disturbances of the stress ₂₂ in a hinge-supported plate are greater than in a rigidly fixed one. Also, it is found that the structural curvings considerably affect the stress distribution in plates both under static and dynamic loading.     

Effect of interphase layers on the elastic properties of a carbon-nanotube-reinforced composite

A variant of a stepwise analysis of the elastic properties of a carbon-nanotube-reinforced composite with account of the effect of interphase layers between the nanotubes and the polymer matrix is reported. The preliminary calculation of the elastic constants of a structural element incorporating a nanotube and an interphase layer and the subsequent calculation of independent elastic constants of a composite with such transversely isotropic structural elements oriented in one direction are both performed by using the Mori–Tanaka theory of an equivalent medium. The calculations are carried out for a wide range of ratios between the elastic moduli of the interphase layer and matrix. The elastic constants of a composite with randomly oriented nanotubes are obtained by using the method of orientational averaging.     

Decreasing the Displacements of a Composite Saddle-Shaped Cable Roof

The structural possibilities of decreasing the compliance of a composite saddle-shaped cable roof having a compliant support contour are investigated. The use of a supporting contour consisting of cables joined together with tie-bars is considered as a structural method enabling one to decrease the compliance of the roof. Each cable of the support has its own initial flexure. The method is most efficient from the viewpoint of material consumption per unit of covered area relative to the increasing rigidity and prestress level of the cable net.The efficiency of the method was evaluated by a numerical experiment, which was carried out for a composite saddle-shaped cable roof 50 × 50 m in the plan. The roof was formed by two orthogonal cable groups joined with a compliant supporting contour. A hybrid composite cable based on a carbon-fiber-reinforced plastic, a glass-fiber-reinforced plastic, and steel was considered as a material for the cable net in combination with steel. The material consumption and the maximum vertical displacement of the cable net in relation to the initial geometrical characteristics of the supporting contour were obtained. A possibility of decreasing the maximum vertical displacements of the roof by 8% was established.     

Numerical-analytical investigation of the stress state of a composite system with phase transitions

Kolosov-Muskhelishvili method is applied to investigate the stress state of a composite system with phase transitions. A technique is proposed for finding the mechanical characteristics of the phase-transition layer and of the composite system as a whole. The results of a numerical experiment are reported for some specific problems.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 62–66, 1986.     

Numerical modeling of nonlinear deformation and buckling of composite plate-shell structures under pulsed loading

Nonlinear three-dimensional problems of dynamic deformation, buckling, and posteritical behavior of composite shell structures under pulsed loads are analyzed. The structure is assumed to be made of rigidly joined plates and shells of revolution along the lines coinciding with the coordinate directions of the joined elements. Individual structural elements can be made of both composite and conventional isotropic materials. The kinematic model of deformation of the structural elements is based on Timoshenko-type hypotheses. This approach is oriented to the calculation of nonstationary deformation processes in composite structures under small deformations but large displacements and rotation angles, and is implemented in the context of a simplified version of the geometrically nonlinear theory of shells. The physical relations in the composite structural elements are based on the theory of effective moduli for individual layers or for the package as a whole, whereas in the metallic elements this is done in the framework of the theory of plastic flow. The equations of motion of a composite shell structure are derived based on the principle of virtual displacements with some additional conditions allowing for the joint operation of structural elements. To solve the initial boundary-value problem formulated, an efficient numerical method is developed based on the finite-difference discretization of variational equations of motion in space variables and an explicit second-order time-integration scheme. The permissible time-integration step is determined using Neumann's spectral criterion. The above method is especially efficient in calculating thin-walled shells, as well as in the case of local loads acting on the structural element, when the discretization grid has to be condensed in the zones of rapidly changing solutions in space variables. The results of analyzing the nonstationary deformation processes and critical loads are presented for composite and isotropic cylindrical shells reinforced with a set of discrete ribs in the case of pulsed axial compression and external pressure.Scientific Research Institute of Mechanics, Lobachevskii Nizhegorodsk State University, N. Novgorod, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 757–776, November–December, 1999.     

Influence of initial stresses on fracture of composite materials containing interacting cracks

Considered in this study are the axially-symmetric problems of fracture of composite materials with interacting cracks, which are subjected to initial (residual) stresses acting along the cracks planes. An analytical approach within the framework of three-dimensional linearized mechanics of solids is used. Two geometric schemes of cracks location are studied: a circular crack is located parallel to the surface of a semi-infinite composite with initial stresses, and two parallel co-axial penny-shaped cracks are contained in an infinite composite material with initial stresses. The cracks are assumed to be under a normal or a radial shear load. Analysis involves reducing the problems to systems of second-kind Fredholm integral equations, where the solutions are identified with harmonic potential functions. Representations of the stress intensity factors near the cracks edges are obtained. These stress intensity factors are influenced by the initial stresses. The presence of the free boundary and the interaction between cracks has a significant effect on the stress intensity factors as well. The parameters of fracture for two types of composites (a laminar composite made of aluminum/boron/silicate glass with epoxy-maleic resin and a carbon/plastic composite with stochastic reinforcement by short ellipsoidal carbon fibers) are analyzed numerically. The dependence of the stress intensity factors on the initial stresses, physical-mechanical parameters of the composites, and the geometric parameters of the problem are investigated.     

Nonlinear homogenization using the nonuniform transformation field analysis

The homogenization of physically nonlinear composite materials with anisotropic morphology is investigated using the nonuniform transformation field analysis (NTFA) first introduced by [1, 2]. In this contribution a three-dimensional finite element implementation (see [3]) of the NTFA is used for the homogenization of composite with morphological anisotropy (see also [4]). The main focus is on the application to structural problems with spatially varying orientation of near-spherical and needle-shaped particle reinforcements. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of a filler on the strength properties of thermosets

The effect of a filler on the strength properties of polymers in tension is investigated. The thermostructural stresses that develop in the composite during cure are taken into account. Relations are given for the strength of the filled polymer as a function of the percentage filler content. In the process of analyzing the thermostructural stresses an analytic expression is obtained for the linear expansion coefficient of the composite with allowance for the structural distribution of the components. Calculated values of the strength and thermostructural stresses are presented for composites with different filler contents. The theoretical determination of the strength of filled polymers is compared with the results of experimental investigations of composites based on epoxy resin filled with quartz dust.Leningrad Mechanical Institute. Translated from Mekhanika Polimerov, No. 1, pp. 97–101, January–February, 1973.     

The likelihood ratio criterion and the asymptotic expansion of its distribution

Summary Asymptotic expansion of the distribution of the likelihood ratio criterion (LRC) for testing a composite hypothesis is derived under null hypothesis and a correction factor ρ which makes the term of order 1/n in the asymptotic expansion of the distribution of it vanish is obtained. The problem is extended to the case of a general composite hypothesis and of Pitman's local alternatives. The asymptotic distribution of LRC for a simple hypothesis is studied under a fixed alternative. The Institute of Statistical Mathematics     

The Superconvergence of the Composite Trapezoidal Rule for Hadamard Finite Part Integrals

The composite trapezoidal rule has been well studied and widely applied for numerical integrations and numerical solution of integral equations with smooth or weakly singular kernels. However, this quadrature rule has been less employed for Hadamard finite part integrals due to the fact that its global convergence rate for Hadamard finite part integrals with (p+1)-order singularity is p-order lower than that for the Riemann integrals in general. In this paper, we study the superconvergence of the composite trapezoidal rule for Hadamard finite part integrals with the second-order and the third-order singularity, respectively. We obtain superconvergence estimates at some special points and prove the uniqueness of the superconvergence points. Numerical experiments confirm our theoretical analysis and show that the composite trapezoidal rule is efficient for Hadamard finite part integrals by noting the superconvergence phenomenon. The work of this author was partially supported by the National Natural Science Foundation of China(No.10271019), a grant from the Research Grants Council of the Hong Kong Special Administractive Region, China (Project No. City 102204) and a grant from the Laboratory of Computational Physics The work of this author was supported in part by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 102204).     

Detection of matrix cracks in composite laminates by using the modal strain energy method

As the foremost mechanism of damage development, matrix cracking is the critical damage found in the early stage of structural failure of composites. This study aims to nondestructively detect matrix cracks in composite laminates by using an experimental modal analysis (EMA). An AS4/PEEK composite was used to fabricate cross-ply [0₂/90₁₂/0₂] and quasi-isotropic [(±45/0/90)₄] _s laminates. The damage in the form of a matrix crack in the laminates was created by using a tensile load. The EMA was conducted on the laminates to obtain the modal displacements before and after damage. The displacements were then employed to compute the modal strain energy and to define the damage index, which is used for detecting matrix cracks. Limited by the mesh points of measurements, we used the differential quadrature method to calculate the partial differentials in the strain energy formula. The results obtained were validated by using the X-ray radiography method and three-point bending tests. The experimental results showed that the damage index well identified the location of breadthwise matrix cracks inside the laminates. However, the resolution of the damage index became poor if the spans of matrix cracks were short or the matrix cracks were scattered over the laminates.     

Variational Treatment and Stability Analysis of Coupled Electro-Mechanics

Dielectric materials such as electro-active polymers (EAPs) belong to the class of functional materials which are used in advanced industrial environments as sensors or actuators and in other innovative fields of research. Driven by Coulomb-type electrostatic forces EAPs are theoretically able to withstand deformations of several hundred percents. However, large actuation fields and different types of instabilities prohibit the ascend of these materials. One distinguishes between global structural instabilities such as buckling and wrinkling of EAP devices, and local material instabilities such as limit- and bifurcation-points in the constitutive response. We outline variational-based stability criteria in finite electro-elastostatics and design algorithms for accompanying stability checks in typical finite element computations. These accompanying stability checks are embedded into a computational homogenization framework to predict the macroscopic overall response and onset of local material instability of particle filled composite materials. Application and validation of the suggested method is demonstrated by a representative model problem. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of Micro- and Macro-Instability Phenomena in Computational Homogenization of Finite Electro-Statics

Dielectric materials such as electro-active polymers (EAPs) belong to the class of functional materials which are used in advanced industrial environments as sensors or actuators and in other innovative fields of research. Driven by Coulomb-type electrostatic forces EAPs are theoretically able to withstand deformations of several hundred percents. However, large actuation fields and different types of instabilities prohibit the ascend of these materials. One distinguishes between global structural instabilities such as buckling and wrinkling of EAP devices, and local material instabilities such as limit- and bifurcation-points in the constitutive response. We outline variational-based stability criteria in finite electro-elastostatics and design algorithms for accompanying stability checks in typical finite element computations. These accompanying stability checks are embedded into a computational homogenization framework to predict the macroscopic overall response and onset of local material instability of particle filled composite materials. Application and validation of the suggested method is demonstrated by representative model problems. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On convergence of the Gauss-Newton method for convex composite optimization

The local quadratic convergence of the Gauss-Newton method for convex composite optimization f=h∘F is established for any convex function h with the minima set C, extending Burke and Ferris’ results in the case when C is a set of weak sharp minima for h. Received: July 24, 1998 / Accepted: November 29, 2000?Published online September 3, 2001     

Study of the physicomechanical properties of various types of biotissues for the purpose of selecting alloprosthetic material

The results of in vitro tests to determine the physicomechanical properties of muscle and fatty tissues, myofascial composite tissues, and the structural soft tissues of the living organism are compared with similar data for unfilled SKTN silicone rubber vulcanizates with different degrees of cross-linking. It is shown that the properties of encapsulated silicone materials are similar to those of myofascial composite tissues tested in vitro. It is proposed to use vulcanizates with a relatively dense vulcanization network, selected on the basis of the modulus of elasticity, for the cosmetic correlation of defects of muscle tissues.     

Numerical realization of the asymptotic averaging method for thermoelastic multidirectional composites

A zero approximation of the asymptotic averaging method is applied to investigate the structural stresses in the structures of spatially reinforced composite materials subjected to mechanical loading and high-temperature heating. A carbon-carbon composite material reinforced with anisotropic fibers in three mutually orthogonal directions in the ratio 111 is considered. According to the averaging method, the local functions, namely the components of the tensors of elastic moduli and thermoelasticity in a zero approximation, must be determined by solving a set of problems for a periodicity cell. The effective thermoelastic constants of the composite are found by averaging the local functions obtained over the periodicity cell. To calculate the structural stresses in constructions, the periodic local functions and the field of macrostrains, which is obtained from the solution of the averaged boundary value problem, must be known. The problems posed for the periodicity cell are solved by the method of finite elements. The average values of the local functions and the measures of deviation from them are examined for various temperatures and volume fractions of fibers of two different cross section shapes.Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 455–464, July–August, 1999.     

Minimally Supported Frequency Composite Dilation Wavelets

A composite dilation wavelet is a collection of functions generating an orthonormal basis for L ²(ℝ ⁿ ) under the actions of translations from a full rank lattice and dilations by products of elements of non-commuting groups A and B. A minimally supported frequency composite dilation wavelet has generating functions whose Fourier transforms are characteristic functions of a lattice tiling set. In this paper, we study the case where A is the group of integer powers of some expanding matrix while B is a finite subgroup of the invertible n×n matrices. This paper establishes that with any finite group B together with almost any full rank lattice, one can generate a minimally supported frequency composite dilation wavelet system. The paper proceeds by demonstrating the ability to find such minimally supported frequency composite dilation wavelets with a single generator.     

Analysis of elastomeric composites based on fiber-reinforced systems. 2. Unidirectional composites

The elastic properties of unidirectionally reinforced composite materials under large deformations are studied. The applied model for deformation of materials is based on the structural macroscopic theory of stiff and soft composites, including micro- and macromechanical levels of analysis of composite media. The properties of unidirectional elastomeric composites are studied in tension and shear in the plane of reinforcement. The microscopic fields in the structural components of composites having poorly compressible and compressible matrices are also analyzed. Changes in the parameters of macroscopic deformation of the composites are examined as functions of the loading parameters and initial conditions of the structure. The evolution of the structural changes in deformed composite materials is described.State Metallurgical Academy of Ukraine, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 29–50, January–February, 1999.     

Microinhomogeneity of a medium as the basis for general methods of modeling the inelastic deformation of a material and a structure

We construct a structural mathematical model for describing the process of inelastic deformation of structural alloys with an arbitrary repeated-variable loading.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 67–71.     

Calculation of deformative and thermal properties of multiphase composite materials filled with composite or hollow spherical inclusions by the effective medium method

A theoretical investigation was carried out to examine the possibilities of a structural approach to prediction of elastic constants, creep functions, and thermal properties of multiphase polymer composite materials filled with composite or hollow spherical Inclusions of several types. The problem of determining effective properties of the composite was solved by generalizing the effective medium method, a variant of the self-consistent method, for the case of a four-phase kernel-shell-matrix-equivalent homogeneous medium model. Exact analytical expressions for the bulk modulus thermal expansion coefficient, thermal conductivity coefficient, and specific heat were obtained. The solution for the shear modulus is given in the form of a nonlinear equation whose coefficients are the solution of a system of 12 linear equations.To be presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October 1995.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 462–472, July–August, 1995.