Showing papers in "International Journal for Computational Methods in Engineering Science and Mechanics in 2013"
TL;DR: The effect of Richardson number ratio of the walls on the laminar mixed convection of a nanofluid flowing in an annulus which was heated uniformly is studied numerically in this article.
Abstract: The effect of Richardson number ratio of the walls on the laminar mixed convection of a nanofluid flowing in an annulus which was heated uniformly is studied numerically. The finite volume technique is utilized to discretize and to solve a set of three-dimensional elliptic governing equations. The secondary flows and contour of the dimensionless axial velocity and dimensionless temperature are presented and discussed. For a given inner or outer wall Ri, the convective heat transfer coefficient of the walls changes differently with Richardson number ratio ( and γ) while inner, outer, and area average friction coefficients do not significantly change. The dimensionless axial velocity profiles shift toward the wall whose Richardson number has a fixed value at the upper vertical plane. The most effect on the axial velocity occurs at the upper vertical plane with respect to or γ. Also, for a given Rii or Rio, the inner and outer wall convective heat transfer coefficient does not increase permanently with incre...
53 citations
TL;DR: The result is a framework for modeling fluid-structure interaction problems with the discontinuity capturing advantages of an integral-based formulation and close correspondence is shown between the proposed method and the classical effective stress principle.
Abstract: Modeling important engineering problems related to flow-induced damage (in the context of hydraulic fracturing among others) depends critically on characterizing the interaction of porous media and interstitial fluid flow. This work presents a new formulation for incorporating the effects of pore pressure in a non-local representation of solid mechanics. The result is a framework for modeling fluid-structure interaction problems with the discontinuity capturing advantages of an integral-based formulation. A number of numerical examples are used to show that the proposed formulation can be applied to measure the effect of leak-off during hydraulic fracturing as well as modeling consolidation of fluid-saturated rock and surface subsidence caused by fluid extraction from a geologic reservoir. The formulation incorporates the effect of pore pressure in the constitutive description of the porous material in a way that is appropriate for nonlinear materials, easily implemented in existing codes, straightforward...
37 citations
TL;DR: A multiscale mechanical model for arterial walls is proposed to describe their age-dependent elastic behavior, highlighting that stiffness of collagen fibrils is related to both cross-link density and their mechanical properties.
Abstract: A multiscale mechanical model for arterial walls is proposed to describe their age-dependent elastic behavior. The model accounts for nanoscale mechanisms related to molecular and cross-link stretching, as well as for micro- and macroscale effects, by employing homogenization techniques. Such a model uses only a few measurable histological parameters, and allows the reproduction of well-established experimental evidence, highlighting that stiffness of collagen fibrils is related to both cross-link density and their mechanical properties. In the case of aortic walls, the model allows to account for histological alterations occurring with age, fully reproducing available experimental results. Proposed evidence also gives a clear mechanical interpretation of the influence of cross-link density and stiffness on arterial tissue elastic modulus and arterial compliance.
34 citations
TL;DR: In this article, the Chebyshev Spectral Collocation Method (CSCM) is applied to two nonlinear boundary value problems in electrohydrodynamic (EHD) ion drag pump flows.
Abstract: The Chebyshev Spectral Collocation Method (CSCM) is applied to two nonlinear boundary value problems in electrohydrodynamic (EHD) ion drag pump flows. We consider two fundamental one-dimensional flows: EHD flow in a conduit and EHD ion drag pumping in a pipe. In the first case, a single dimensionless momentum equation for axial flow velocity is considered. In the second case, three coupled equations for electrical field, potential and charge density are considered. Both models comprise ordinary differential equations. The present study finds applications in micro-fabrication and biomicrofluidic systems. The excellent accuracy and potential of CSCM in nonlinear electro-hydrodynamics is demonstrated.
34 citations
TL;DR: In this paper, a finite element model is proposed for the study of two-dimensional arch structures, which is irrispective of the shape of the arch and capable of analyzing thick to very thin structures using a modified Mindlin-Reissner theory.
Abstract: In this paper, a finite element model is proposed for the study of two-dimensional arch structures. Three- and five-node elements are developed irrispective of the shape of the arch and capable of analyzing thick to very thin structures using a modified Mindlin-Reissner theory. A compatibility displacement-based method is used: full integration is introduced to evaluate all energy terms and the convergence pattern is completely independent of the thickness values, even if a coarse mesh is employed. Shear and membrane locking are completely eliminated, shaping shear and membrane strains by means of suitable functions appropriately projected over Gauss integration points. A formulation has been developed which takes into account, in the elastic range, the possibility of working with a more general cross-section conceived as a set of layers. Numerical examples are also given to show the accuracy of the method and comparisons with previous models are made.
21 citations
TL;DR: In this article, a switching implicit-explicit algorithm embedded into the finite element method was used to solve the divergence problem of an elastic-plastic arch in finite element analysis.
Abstract: In this paper, we present a study of finite element analysis (FEA) of structural instability by using a switching implicit-explicit algorithm embedded into the finite element method. Snap-through or snap-back buckling problems often cause divergence of the finite element method if arc-length methods are not used. The origin of divergence is often associated with critical points. An alternative to the latter is considered herein, the implicit–explicit FEA. The numerical results showed the effectiveness of this switching technique for solving divergence when simulating structural instabilities such as buckling of an elastic–plastic arch.
20 citations
TL;DR: In this article, a new numerical methodology is developed to infer the shape a heated body should have for the temperature distribution on part of its boundary to match a prescribed one, which enables a simple discretization of the Heat Equation using finite differences and allows us to remesh the physical domain, which varies at each optimization iteration.
Abstract: This paper deals with an inverse steady-state heat transfer problem. We develop in this work a new numerical methodology to infer the shape a heated body should have for the temperature distribution on part of its boundary to match a prescribed one. This new numerical methodology solves this shape optimization problem using body-fitted grid generation to map the unknown optimal shape onto a fixed computational domain. This mapping enables a simple discretization of the Heat Equation using finite differences and allows us to remesh the physical domain, which varies at each optimization iteration. A novel aspect of this work is the sensitivity analysis, which is expressed explicitly in the fixed computational domain. This allows a very efficient evaluation of the sensitivities. The Conjugate Gradient method is used to minimize the objective function and this work proposes an efficient redistribution method to maintain the quality of the mesh throughout the optimization procedure.
19 citations
TL;DR: Vibration suppression of a smart thin elastic rectangular plate is considered and a nonlinear controller is designed, based on fuzzy inference, which is employed for time integration.
Abstract: Vibration suppression of a smart thin elastic rectangular plate is considered. The plate is subjected to external disturbances and generalized control forces, produced, for instance, by electromechanical feedback. A nonlinear controller is designed, based on fuzzy inference. The initial-boundary value problem is spatially discretized by means of the time spectral method. The implicit Newmark-beta method is employed for time integration. Two numerical algorithms are proposed. The techniques have been implemented within MATLAB with the use of the Fuzzy Logic Toolbox. Representative numerical results are given.
17 citations
TL;DR: In this paper, the Laplace transform is used to transform the coupled equations into a Laplace transformed domain and numerical inversion of the transform is carried out using Fourier series expansion techniques.
Abstract: This paper deals with the thermoelastic interactions in a transversely isotropic, infinite hollow cylinder in which the boundaries are stress-free. There is no temperature in the inner boundary and heat flux is applied on the outer boundary. In the context of two-temperature generalized thermoelasticity theory, the three-phase-lag thermoelastic model and Green Naghdi model III (GN-III) are employed to study the thermophysical quantities. The Laplace transform is used to transform the coupled equations into the Laplace transformed domain. Then two different methods, the Galerkin finite element technique and eigen-value approach, are employed to solve the resulting equations in the transformed domain. The numerical inversion of the transform is carried out using Fourier-series expansion techniques. The physical quantities have been computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (GN-III and three-phase-lag model) and for two different...
16 citations
TL;DR: In this article, a three-dimensional elliptic grid generation technique was used to generate a mesh over the body and solve for a heat conduction equation, and a novel sensitivity analysis scheme was proposed to compute the sensitivity of the temperatures to variation of grid node positions and the conjugate gradient method was used as an optimization algorithm to minimize the difference between the computed temperature on the boundary and desired temperature.
Abstract: This paper is concerned with an optimal shape design (shape optimization) problem in heat transfer. As an inverse steady-state heat transfer problem, given a body locally heated by a specified heat flux and exposed to convective heat transfer on parts of its boundary, the aim is to find the optimal shape of this body such that the temperature is constant on a desired subset of its boundary. The numerical method to achieve this aim consists of a three-dimensional elliptic grid generation technique to generate a mesh over the body and solve for a heat conduction equation. This paper describes a novel sensitivity analysis scheme to compute the sensitivity of the temperatures to variation of grid node positions and the conjugate gradient method (CGM) is used as an optimization algorithm to minimize the difference between the computed temperature on the boundary and desired temperature. The elliptic grid generation technique allows us to map the physical domain (body) onto a fixed computational domain and to d...
15 citations
TL;DR: In this article, the axisymmetric problem is formulated in terms of a second-order ordinary differential equation, which is solved by employing the finite element method (FEM) and the temperature profile has been modeled with the help of a heat conduction equation.
Abstract: This paper studies the thermoelastic displacements, stresses, and strains in a thin, circular, functionally graded material (FGM) disk subjected to thermal load by taking into account an inertia force due to rotation of the disk. The material properties of the FGM disk have been assumed to vary exponentially in the radial direction. Based on the two-dimensional thermoelasticity theory, the axisymmetric problem is formulated in terms of a second-order ordinary differential equation, which is solved by employing the finite element method (FEM). The temperature profile has been modeled with the help of a heat conduction equation. The model has been solved numerically to attain stresses, strains, and displacements in an Al2O3/Al FGM circular disk and the computer-simulated results are presented graphically. The effect of Kibel Number on stresses, strains, and displacement has also been discussed. The numerical results reveal that these quantities are significantly influenced by temperature distribution, thick...
TL;DR: In this article, the degradation of concrete dams with age was investigated and an isotropic degradation index was introduced to evaluate the nonlinear seismic response of the dams to future earthquake forces.
Abstract: The design of a concrete gravity dam must provide the ability to withstand the seismic forces for which nonlinear behavior is expected. The nonlinear seismic response of the dam may be different due to aging, as the concrete gets degraded because of environmental factors and mechanical loadings. The present study investigates the evolution of tensile damages in aged concrete gravity dams, which is necessary to estimate the safety of existing dams towards future earthquake forces. The degraded material properties of the concrete with age, subjected to environmental factors and mechanical loadings, are determined introducing an isotropic degradation index. A concrete damaged plasticity model, which assumes both the compressive and tensile damage, is used to evaluate the nonlinear seismic response of the dam. Results show that the peak maximum principal stresses reduced at the neck due to aging effects in the concrete. It is observed that the neck region is the most vulnerable region to initiate damage for a...
TL;DR: In this article, the structural optimization of an axial flow compressor rotating disk in a more simplistic way has been studied, where FEA is completely avoided during the optimization runs with the help of response equations.
Abstract: This study is focused on the structural optimization of an axial flow compressor rotating disk in a more simplistic way. Since optimization involves several runs, performing Finite Element Analysis (FEA) for a disk model in each run increases computational cost. Alternative response surface design models have been developed using the design of experiment (DOE) method to represent the FE disk model. These response equations are validated and used in optimization runs. A constraint nonlinear optimization procedure based on genetic algorithms has been used. FEA is completely avoided during the optimization runs with the help of response equations, resulting in less computational time and cost.
TL;DR: In this paper, uncertainties in composite material properties at the ply-level can lead to undesirable couplings in laminates designed with no couplings, where couplings are introduced deliberately for structural or aeroelastic tailoring.
Abstract: Elastic couplings can strongly effect the structural behavior of composites by their presence or absence. We show that uncertainties in composite material properties at the ply-level can lead to undesirable couplings in laminates designed with no couplings. Moreover, uncertainty can alter the couplings in lay-ups where couplings are introduced deliberately for structural or aeroelastic tailoring. For numerical results, a symmetric balanced and an unsymmetric unbalanced laminate are considered. Material uncertainties are numerically quantified using Monte Carlo simulations for different number of plies, ply angles, and loading conditions and their effect is found to be substantial.
TL;DR: In this paper, the effect of inhomogeneities (holes, cracks, inclusions) on an edge crack has been studied by the extended finite element method (XFEM).
Abstract: In this work, the effect of inhomogeneities (holes, cracks, inclusions) on an edge crack has been studied by the extended finite element method (XFEM). In XFEM, finite element approximation is enriched by additional functions using partition of unity. The level set method is used for tracking the location of holes, cracks, and inclusions. The multiple discontinuities of random size (in a given range) are arbitrarily distributed in the plate/domain. The values of stress intensity factors (SIFs) are extracted from the XFEM solution by domain-based interaction integral approach. These simulations show that the presence of inhomogeneities has a significant effect on SIFs.
TL;DR: In this paper, a new, proposed, ultrasonic assisted EDM is investigated, where the problem is assumed to be axisymmetric and simultaneous ultrasonic vibration of the tool and the workpiece increases the lifetime of the bubble and its growth and collapse rates.
Abstract: In this paper, a new, proposed, ultrasonic assisted EDM is investigated. The problem is assumed to be axisymmetric. Results show that simultaneous ultrasonic vibration of the tool and the workpiece increases the lifetime of the bubble and its growth and collapse rates. Results also show that simultaneous ultrasonic vibration of the tool and the workpiece causes the vapor bubble to expand to a larger maximum volume. This, in turn, causes the pressure inside the vapor bubble to drop to a lower minimum volume, facilitates the ejection of the molten material from the crater, and enhances the material removal rate.
TL;DR: In this article, the authors analyzed the behavior of MWCNTs composition for polycarbonate composites under both static and impact loads, and they found that an optimum composition of 2.1 weight % of polycarbonates exhibits maximum stress resistance within elastic range under strain rates of nearly 2500/s.
Abstract: High strain rate experiments performed on multi-walled carbon nanotubes, polycarbonate composites (MWCNT-PC) have exhibited enhanced impact resistance under a dynamic strain rate of nearly 2500/s with composition of only 0.5 to 2.0% multi-walled carbon nanotubes (MWCNTs) in pure polycarbonate (PC). Similarly, hardness and elastic modulus under static loads resulted in a significant increase, depending upon the composition of MWCNTs in PC. The present work aims to analyze these results by correlating the data to fit expressions in generalizing the behavior of MWCNTs composition for MWCNT-PC composites under both static and impact loads. As a result, we found that an optimum composition of 2.1 weight % of MWCNTs exhibits maximum stress resistance within elastic range under strain rates of nearly 2500/s for MWCNT-PC composites. The composition of MWCNTs plays a crucial role in maximizing modification of static and dynamic impact-based mechanical properties of polycarbonates. Further, a simple model based on ...
TL;DR: In this paper, the influence of thermal and thermo diffusion on convection heat and mass transfer in an electrically conducting power law flow over a heated porous plate in the presence of magnetic field has been considered.
Abstract: In this paper, the influence of thermal and thermo diffusion on convection heat and mass transfer in an electrically conducting power law flow over a heated porous plate in the presence of magnetic field has been considered. The similarity solution is used to transform the system of partial differential equations into a boundary value problem of coupled ordinary differential equations. Runge Kutta of sixth order has been used along with a shooting method for better accuracy. The results were presented as velocity, temperature, and concentration fields for pseudoplastic and dilatant fluids for different values of the embedded flow parameters. The results are presented graphically and the conclusion is drawn that the flow field and other quantities of physical interests are significantly influenced by these parameters.
TL;DR: In this article, the stochastic postbuckling response of elastically supported FGM plate with random system properties subjected to uniform and nonuniform temperature change with temperature-dependent and -independent material properties is presented.
Abstract: This paper presents the stochastic post-buckling response of elastically supported FGM plate with random system properties subjected to uniform and nonuniform temperature change with temperature-dependent and -independent material properties. The FGMs plate is supported with two parameters of Pasternak foundation with Winkler cubic nonlinearity. The basic formulation is based on higher-order shear deformation theory (HSDT) with von-Karman nonlinearity using modified C0 continuity. A direct iterative-based nonlinear finite element method combined with first-order perturbation technique is used to compute the second-order statistics (mean and coefficient of variation) of post-buckling response of FGM plates.
TL;DR: In this article, the effects of thermal and solutal stratification on natural convection along a vertical plate embedded in a micropolar fluid are analyzed in both cases of buoyancy-assisting and buoyancyopposing flows.
Abstract: The effects of thermal and solutal stratification on natural convection along a vertical plate embedded in a micropolar fluid are analyzed in both cases of buoyancy-assisting and buoyancy-opposing flows. The nonlinear governing equations and their associated boundary conditions are initially cast into dimensionless forms by pseudo-similarity variables. The resulting system of equations is then solved numerically using the Keller-box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The velocity, microrotation, temperature, and concentration profiles are shown for different values of the coupling number, thermal, and solutal stratification parameters. The numerical values of the skin friction, wall couple stress, heat and mass transfer rates for different values of governing parameters are also tabulated.
TL;DR: In this article, the exact solutions of eigenfrequencies and vibration modes of rectangular cantilever thin plates are derived by using the double finite integral transform method, which eliminates the need to predetermine the deformation function arbitrarily and is hence more reasonable than conventional semi-inverse methods.
Abstract: Exact solutions of eigenfrequencies and vibration modes of rectangular cantilever thin plates are derived by using the double finite integral transform method. Since only the basic elasticity equations of the plates are used, the analytical method utilized in this paper eliminates the need to predetermine the deformation function arbitrarily and is hence more reasonable than conventional semi-inverse methods. Numerical results presented in the paper demonstrate the validity of the approach.
TL;DR: In this article, steady simulations were performed to investigate tip leakage flow and heat transfer characteristics on the rotor blade tip and casing in a single-stage gas turbine engine, and it was observed that the tip leakage flows structure is highly dependent on the height of the tip gap and the speed of the rotor.
Abstract: Steady simulations were performed to investigate tip leakage flow and heat transfer characteristics on the rotor blade tip and casing in a single-stage gas turbine engine. A typical high-pressure gas turbine stage was modeled with a pressure ratio of 3.2. The predicted isentropic Mach number and adiabatic wall temperature on the casing showed good agreement with available experimental data under similar operating condition. The present numerical study focuses extensively on the effects of tip clearance heights and rotor rotational speeds on the blade tip and casing heat transfer characteristics. It was observed that the tip leakage flow structure is highly dependent on the height of the tip gap and the speed of the rotor. In all cases, the tip leakage flow was seen to separate and recirculate just around the corner of the pressure side of the blade tip. This region of re-circulating flow enlarges with increasing clearance heights. The separated leakage flow reattaches afterwards on the tip surface. Leakag...
TL;DR: In this paper, a volume-reinitialization scheme was proposed to correct the volume loss of the level set method in multiphase flows by solving an appropriate equation for level set function after every time step.
Abstract: Despite the inherent advantages of the level set method in the computation of multiphase flows, the principal drawback has been the lack of conservation of mass (or volume in incompressible flows). While the level set community has resorted to the use of highly accurate schemes like a fifth-order Weighted Essentially Non-Oscillatory (WENO) scheme for the solution of level set equations, it is seen that for certain classes of problems the volume loss is still high. In order to circumvent this limitation of the level set method, in this paper we propose a volume-reinitialization scheme, wherein volume correction is accomplished by solving an appropriate equation for level set function after every time step. The volume-reinitialization scheme recognizes the local curvature of the interface while correcting the volume loss. The efficacy of the proposed technique has been tested for several problems that include determination of equilibrium shape of free surface in a rotating cylindrical container and simulati...
TL;DR: In this article, the authors studied two cases of high blowing ratio (off-design condition) of 2.0 and l 1.5, respectively, where the film is likely to be detached from the surface.
Abstract: Film cooling is used in a wide range of industrial and engineering applications; one of the most important is in gas turbine cooling. The intent of film cooling is to provide a layer of cool film between the surface and the hot gas. Predicting film-cooling characteristics, particularly at high blowing ratios where the film is likely to be detached from the surface, is a challenge due to the complex three-dimensional and possibly anisotropic nature of the flow. Despite the growth of more sophisticated techniques for modeling turbulence, such as large eddy simulation (LES), the most commonly used methods in design are Reynolds-Averaged Navier Stokes (RANS) methods that employ a two-equation turbulence model for specifying the eddy viscosity. Although these models have deficiencies, they continue to be used throughout industry because they offer reasonable turnaround time as compared to LES or other methods. This paper studies in detail two cases, one of high blowing ratio (off-design condition) of 2.0 and l...
TL;DR: In this paper, the free vibration of monolayer graphene sheets is studied on the basis of a nonlocal elastic plate model, and an explicit formula for estimating the fundamental frequencies of a monoleayer graphene sheet from its static deflection under a uniformly distributed load is obtained.
Abstract: In this work, on the basis of a nonlocal elastic plate model, the free vibration of monolayer graphene sheets is studied. An explicit formula for estimating the fundamental frequencies of a monolayer graphene sheet from its static deflection under a uniformly distributed load is obtained. The main advantage of this formula is in its simplicity and accuracy, enabling quick calibration of the nonlocal parameter using molecular dynamics results. The influences of the nonlocality and boundary conditions on the free vibration of monolayer graphene sheets are also investigated.
TL;DR: In this article, the effects of radial point interpolation method (RPIM) shape parameters on the solution accuracy of 2D elastoplastic problems are investigated and the convergence rates after yielding are investigated for perfectly plastic and hardening cases with various shape parameters.
Abstract: The effects of radial point interpolation method (RPIM) shape parameters on the solution accuracy of 2D elastoplastic problems are investigated. The RPIM algorithm is adapted for the solution of 2D elastoplastic problems using the multi-quadric radial basis function. The convergence rates after yielding are investigated for perfectly plastic and hardening cases with various shape parameters. Both regular and irregular node distributions are used by considering the standard Gauss integration and nodal integration schemes. It is shown that the solutions after yielding can be improved using appropriate shape parameters. The propagation of plastic region and solution time of each case are presented against load increments.
TL;DR: Experimental results demonstrate that the proposed algorithm is powerful enough to recover the missing shape, and the resulted patching meshes interpolate the shape and density of the surrounding mesh and naturally blend with it, which are of good quality for engineering.
Abstract: The hole-free triangular mesh model is a prerequisite for many applications. In this paper, we propose a novel hole-filling algorithm for triangular meshes in engineering which can recover the geometric features of the original meshes. Firstly, the sharp vertices around the hole are extracted and classified into different feature sets. Then the sharp vertex sets are used to construct feature curves with missing parts in the hole by cubic spline interpolation. These feature curves divide the original complex hole into small, flatter sub-holes. Finally, each sub-hole is triangulated into a set of new triangles, and a series of iterative modifications are employed to refine and improve the geometry of hole according to the properties of surrounding mesh. Experimental results demonstrate that the proposed algorithm is powerful enough to recover the missing shape, and the resulted patching meshes interpolate the shape and density of the surrounding mesh and naturally blend with it, which are of good quality fo...
TL;DR: In this article, a finite element contact analysis of a functionally graded (FG) brake disk in contact with a pad, subjected to rotation, contact pressure, and frictional heat, is presented.
Abstract: In this paper, finite element contact analysis of a functionally graded (FG) brake disk in contact with a pad, subjected to rotation, contact pressure, and frictional heat, is presented. The material properties vary through the thickness according to a power-law characterized by a grading index, n. The contact surfaces are full-ceramic with full-metal free surface. The effects of n on the displacement, contact status, strain and stress are investigated. From the analysis, thermo-elastic and contact results are extremely dependent on n. Hence, n is an important criteria for the design of FG brake disks for automotive and aircraft applications.
TL;DR: It is the duty, therefore, to reiterate the whys and hows of parameterization of intervals, introduced in [1] to incorporate the possibly available information on dependencies between various intervals describing the problem at hand.
Abstract: Novel elements of the parameterized interval analysis developed in [1, 2] are emphasized in this response, to Professor E.D. Popova, or possibly to others who may be perplexed by the parameterized interval analysis. It is also shown that the overwhelming majority of comments by Popova [3] are based on a misreading of our paper [1]. Partial responsibility for this misreading can be attributed to the fact that explanations provided in [1] were laconic. These could have been more extensive in view of the novelty of our approach [1, 2]. It is our duty, therefore, to reiterate, in this response, the whys and hows of parameterization of intervals, introduced in [1] to incorporate the possibly available information on dependencies between various intervals describing the problem at hand. This possibility appears to have been discarded by the standard interval analysis, which may, as a result, lead to overdesign, leading to the possible divorce of engineers from the otherwise beautiful interval analysis.
TL;DR: In this paper, a solution of the Lame problem on equilibrium of an elastic parallelepiped using the complete systems method is presented, which makes it possible to reduce the initial three-dimensional problem to a new structure, which is the system of three interconnected one-dimensional problems.
Abstract: The paper presents a solution of the Lame problem on equilibrium of an elastic parallelepiped using the complete systems method. The feature of the method lies in the fact that it makes it possible to reduce the initial three-dimensional problem to a new structure, which is the system of three interconnected one-dimensional problems. The solutions obtained by the technique developed reveal high accuracy compared with solutions of the Lame problem by other methods. This fact supports the efficiency of the approach used. The algorithm developed is employed to evaluate approximate models of the elasticity theory using, as an example, determining stiffness of vibroinsulators.