Showing papers on "Direct stiffness method published in 2009"
TL;DR: A new stiffness modeling method for overconstrained parallel manipulators with flexible links and compliant actuating joints is presented, based on a multidimensional lumped-parameter model that replaces the link flexibility by localized 6-dof virtual springs that describe both translational/rotational compliance and the coupling between them.
271 citations
TL;DR: The ElastoDynamics Toolbox (EDT) version 2.1 offers an extensive set of MATLAB functions to model elastodynamic wave propagation in horizontally layered media based on the direct stiffness method and the thin layer method, which are formulated in the frequency-wavenumber domain.
110 citations
TL;DR: In this article, the stiffness of a 5-DOF hybrid machine tool with actuation redundancy is analyzed and an accurate stiffness model of the machine tool is derived by using the assembly method.
94 citations
TL;DR: This paper addresses linear algebra aspects of this new finite element method for the discretization of elliptic partial differential equations on surfaces and proves that the (effective) spectral condition number of the diagonsally scaled mass matrix and the diagonally scaled stiffness matrix behaves like h.
Abstract: We consider a recently introduced new finite element approach for the discretization of elliptic partial differential equations on surfaces. The main idea of this method is to use finite element spaces that are induced by triangulations of an “outer” domain to discretize the partial differential equation on the surface. The method is particularly suitable for problems in which there is a coupling with a problem in an outer domain that contains the surface, for example, two-phase flow problems. It has been proved that the method has optimal order of convergence both in the H 1 and in the L 2-norm. In this paper, we address linear algebra aspects of this new finite element method. In particular the conditioning of the mass and stiffness matrix is investigated. For the two-dimensional case we present an analysis which proves that the (effective) spectral condition number of the diagonally scaled mass matrix and the diagonally scaled stiffness matrix behaves like h −3| ln h| and h −2| ln h|, respectively, where h is the mesh size of the outer triangulation.
75 citations
TL;DR: In this paper, a three-dimensional NMM based on tetrahedral meshes is developed, where the displacement functions of manifold elements are formulated by the partition of unity function, and the global equilibrium equations for three dimensional elasto-statics problem are established by minimizing the total potential energy.
60 citations
10 Oct 2009
TL;DR: A systematic elasto-geometrical modeling method is used to derive the analytical manipulator stiffness models by taking into account their link and joint compliances, which can be applied to any serial and parallel manipulators for which stiffness is a critical issue.
Abstract: This paper presents the design optimization of a Delta-like robot manipulator with respect to multiple global stiffness objectives For this purpose, a systematic elasto-geometrical modeling method is used to derive the analytical manipulator stiffness models by taking into account their link and joint compliances The models are then involved within a statistically sensitivity analysis of the influence of the geometric parameters on four global indices that describe the structure stiffness over the workspace Multi-Objective Genetic Algorithm, ie Pareto-optimization, is taken as the appropriate framework for the definition and the solution of the addressed multi-objective optimization problem Our approach is original in the sense that it is systematic and it can be applied to any serial and parallel manipulators for which stiffness is a critical issue
59 citations
TL;DR: In this article, the stiffness model of a 3DOF Tricept robot with a properly constrained passive limb is formulated using the 6×6 overall Jacobian and the stiffness evaluation of a sample tricept is carried out using two global indices obtained from singular value decomposition of the compliance matrix.
Abstract: Taking the 3DOF parallel mechanism within the Tricept robot as an example, this paper presents an analytical approach for the stiffness modeling of parallel kinematic machines having a properly constrained passive limb. The stiffness model is formulated using the 6×6 overall Jacobian. It takes particular interest in the precise formulation of the bending stiffness matrix of the properly constrained passive limb by considering the compatibility conditions of the system. Stiffness evaluation of a sample Tricept robot is carried out using two global indices obtained from singular value decomposition of the compliance matrix.
59 citations
TL;DR: In this paper, the design formulation of compliant mechanisms is posed as a topology optimization problem, where the stiffness matrix of a single-input, single-output (SISO) mechanism is represented by the stiffness matrices of its structure with respect to the input-output ports.
Abstract: This article focuses on design formulation of compliant mechanisms posed as a topology optimization problem. With the use of linear elasticity theory, a single-input, single-output compliant mechanism is represented by the stiffness matrix of its structure with respect to the input–output ports. It is shown that the stiffness model captures the intrinsic stiffness properties of the mechanism. Furthermore, in order for the optimization problem to be properly defined, it is necessary that the stiffness matrix of the mechanism's structure must be guaranteed to be always positive definite. An exploratory design formulation is then presented based on this necessary condition. Numerical examples are provided to illustrate the potential benefits of using the intrinsic stiffness properties for compliant mechanism design with topology optimization techniques.
54 citations
TL;DR: It is shown that a few universal geometric quantities have the same dominant effect on the stiffness matrix conditioning for different finite element spaces for both linear algebraic solvers and the unstructured geometric meshing.
Abstract: The performance of finite element computation depends strongly on the quality of the geometric mesh and the efficiency of the numerical solution of the linear systems resulting from the discretization of partial differential equation (PDE) models. It is common knowledge that mesh geometry affects not only the approximation error of the finite element solution but also the spectral properties of the corresponding stiffness matrix. In this paper, for typical second-order elliptic problems, some refined relationships between the spectral condition number of the stiffness matrix and the mesh geometry are established for general finite element spaces defined on simplicial meshes. The derivation of such relations for general high-order elements is based on a new trace formula for the element stiffness matrix. It is shown that a few universal geometric quantities have the same dominant effect on the stiffness matrix conditioning for different finite element spaces. These results provide guidance to the studies of both linear algebraic solvers and the unstructured geometric meshing.
54 citations
TL;DR: In this article, the authors present an efficient computer method for inelastic and large deflection analysis of steel space frames with non-linear flexible joint connections, based on the most refined type of second-order analysis, the plastic zone analysis.
51 citations
TL;DR: In this paper, a dynamic stiffness method is introduced to investigate the free vibration of laminated composite beams based on a third-order shear deformation theory which accounts for parabolic distribution of the transverse shear strain through the thickness of the beam.
Abstract: The dynamic stiffness method is introduced to investigate the free vibration of laminated composite beams based on a third-order shear deformation theory which accounts for parabolic distribution of the transverse shear strain through the thickness of the beam. The exact dynamic stiffness matrix is found directly from the analytical solutions of the basic governing differential equations of motion. The Poisson effect, shear deformation, rotary inertia, in-plane deformation are considered in the analysis. Application of the derived dynamic stiffness matrix to several particular laminated beams is discussed. The influences of Poisson effect, material anisotropy, slenderness and end condition on the natural frequencies of the beams are investigated. The numerical results are compared with the existing solutions in literature whenever possible to demonstrate and validate the present method.
TL;DR: In this paper, the authors present an efficient way of implementing general multi-point constraint conditions in a finite element solver, where all constrained degrees of freedoms are already eliminated during the assembly of the global stiffness matrix and right-hand side vectors.
TL;DR: In this article, a modeling technique based on the direct stiffness method (DSM) was proposed to describe the behavior in time of composite beams with partial shear interaction accounting for creep and shrinkage of the slab.
Abstract: This paper presents a modelling technique based on the direct stiffness method (DSM) to describe the behaviour in time of composite beams with partial shear interaction accounting for creep and shrinkage of the slab. The time-dependent behaviour of the concrete is modelled using algebraic representations, such as the age-adjusted effective modulus method and the mean stress method, while the steel joist, the reinforcement and the shear connection are assumed to behave in a linear-elastic manner. Only one discretization (i.e. in the time domain) is required by the proposed stiffness formulations to perform a time analysis, while two discretizations (i.e. one in the time domain and the other in the spatial domain along the beam axis) are required by other modelling techniques available in the literature. The ability of the derived elements to overcome curvature locking problems observed to occur in some conventional displacement formulations is also highlighted. The proposed DSM approach is then validated against analytical solutions derived by the authors for simple structural systems. The applicability of this method for the time analysis of continuous composite beams is also illustrated. Copyright © 2008 John Wiley & Sons, Ltd.
01 Jan 2009
TL;DR: A stiffness analysis of a 6-RSS parallel architecture by using matrix structural analysis based on standard concepts of static elastic deformations to obtain the stiffness matrix that can be numerically computed by defining a suitable model of the manipulator.
Abstract: This paper describes a stiffness analysis of a 6-RSS parallel architecture by using matrix structural analysis. The stiffness analysis is based on standard concepts of static elastic deformations. The formulation has been implemented in order to obtain the stiffness matrix that can be numerically computed by defining a suitable model of the manipulator, which takes into account the stiffness properties of each element such as links, actuators and joints. In order to simplify the model, joints and actuators stiffness have been neglected. The obtained stiffness matrix was used to map the end-effector compliant displacements when external forces and torques are applied on it.
TL;DR: In this paper, the stiffness matrix is expressed in terms of the screw coordinates with respect to the basis consisting of its eigenvectors, and the synthesis equation is derived, which allows one to select the positions or directions of the springs from the screw system spanned by the induced wrenches of the given stiffness matrix.
Abstract: It is possible to realize the desired compliance characteristics of a robot in a form of a passive compliance device, which demands the synthesis technique of a stiffness matrix by parallel connections of line and/or torsional springs. In this paper, the stiffness matrix is expressed in terms of the screw coordinates with respect to the basis consisting of its eigenvectors, thereby the synthesis equation is derived. Examination of the numbers of free design parameters involved in the synthesis suggests that a line or free vector for a spring can be freely selected from the induced wrench space depending on the rank of the stiffness matrix. The recursive synthesis method that allows one to select the positions or directions of the springs from the screw system spanned by the induced wrenches of the given stiffness matrix is proposed.
TL;DR: In this paper, the authors derived the finite element of a beam with an arbitrary number of transverse cracks, where each crack is replaced by a corresponding linear rotational spring connecting two adjacent elastic parts.
TL;DR: In this paper, a parametric finite-volume direct averaging micromechanics theory for periodic materials is employed to investigate the effective moduli and thermal expansion coefficients of lamellar composites with wavy architectures.
Abstract: The recently developed parametric finite-volume direct averaging micromechanics theory for periodic materials is employed to investigate the effective moduli and thermal expansion coefficients of lamellar composites with wavy architectures. In the parametric version, a reference square subvolume is mapped onto a quadrilateral subvolume in the actual discretized microstructure to accurately capture the in situ microstructural details. The mapping is used to construct local stiffness matrices of quadrilateral subvolumes which are employed in the local/global stiffness matrix solution strategy for the unit cell problem within a homogenization framework. Complete set of homogenized moduli and thermal expansion coefficients of multilayers comprised of alternating soft and hard laminae with two types of waviness is generated for the first time as a function of the volume content of the hard phase for two amplitude-to-wavelength ratios. The observed changes in the homogenized mechanical and thermal properties relative to the reference flat-layer configuration depend on the wavy microstructure orientation and become greater with increasing amplitude-to-wavelength ratios. Examination of local stress fields explains the differences observed in the homogenized moduli of multilayers with sinusoidal and corrugated waveforms for the two amplitude-to-wavelength ratios.
01 Feb 2009
TL;DR: In this paper, a finite-element model is presented to reproduce the behaviour of the torsional stiffness of a harmonic drive (HD) and the model allows an evaluation of the effects of various geometrical constraints.
Abstract: Torsional stiffness or rigidity is a crucial characteristic in the design of transmission devices, including harmonic drives (HDs). Among the various design aspects constituting a reduction mechanism in robotic systems, torsional stiffness is an important factor for positioning accuracy and control issues. One of the major advantages of HDs is their capacity to present a high reduction ratio while maintaining a small hardware size. However, manufacturing these drives remains a complex and costly process due to the high precision of its machined components; as a result, the use of such drives is still limited only to high-end mechanical products and technologies. Given these costs, numerical analysis becomes an effective alternative for obtaining valuable data through simulations, without the need for prototypes. This article presents a finite-element model to reproduce the behaviour of the torsional stiffness of an HD. The numerical model allows an evaluation of the effects of various geometrical ...
TL;DR: In this paper, the authors considered non-proportional damping in linear damped vibrating systems in which the stiffness and damping matrices are not restricted to being symmetric and positive definite.
Abstract: This note deals with three aspects of nonproportional damping in linear damped vibrating systems in which the stiffness and damping matrices are not restricted to being symmetric and positive definite First, we give results on approximating a general damping matrix by one that commutes with the stiffness matrix when the stiffness matrix is a general diagonalizable matrix, and the damping and stiffness matrices do not commute The criterion we use for carrying out this approximation is closeness in Euclidean norm between the actual damping matrix and its approximant When the eigenvalues of the stiffness matrix are all distinct, the best approximant provides justification for the usual practice in structural analysis of disregarding the off-diagonal terms in the transformed damping matrix However, when the eigenvalues of the stiffness matrix are not distinct, the best approximant to a general damping matrix turns out to be related to a block diagonal matrix, and the aforementioned approximation cannot be justified on the basis of the criterion used here In this case, even when the damping and stiffness matrices commute, decoupling of the modes is not guaranteed We show that for general matrices, even for symmetric ones, the response of the approximate system and the actual system can be widely different, in fact qualitatively so Examples illustrating our results are provided Second, we present some results related to the difficulty in handling general, nonproportionally damped systems, in which the damping matrix may be indefinite, by considering a simple example of a two degrees-of-freedom system Last, we use this example to point out the nonintuitive response behavior of general nonproportionally damped systems when the damping matrix is indefinite Our results point to the need for great caution in approximating nonproportionally damped systems by damping matrices that commute with the stiffness matrix, especially when considering general damping matrices Such approximations could lead to qualitatively differing responses between the actual system and its proportionally damped approximation
TL;DR: In this paper, the authors presented a new methodology that is more straightforward and simpler than existing techniques for computing the tangent stiffness matrix of a multi-degree-of-freedom (dof) test specimen.
Abstract: Researchers have long recognized the importance and potential benefits of utilizing the tangent stiffness matrix of a test specimen in hybrid simulations employing implicit and mixed-integration schemes. However, the computation of the tangent stiffness matrix during testing has proved to be challenging, particularly for test specimens with more than one degree of freedom (dof). This paper presents a new methodology that is more straightforward and simpler than existing techniques for computing the tangent stiffness matrix of a multi-dof test specimen. The proposed method is combined with the operator-splitting method (OSM), and the capabilities, advantages and limitations of the new formulation are demonstrated through several examples. The accuracy, stability, and error propagation characteristics of the modified OSM are also studied theoretically as well as numerically. The research results show that the proposed algorithm provides results that are better than those produced via the regular OSM alone, especially for damped structures undergoing highly inelastic behavior during testing.
TL;DR: In this article, the accuracy of the finite element method and strip method of analysis for calculating the lateral stiffness of steel plate shear wall (SPSW) systems is assessed by making comparisons with experimental findings.
Abstract: The accuracy of the finite element method and strip method of analysis for calculating the lateral stiffness of steel plate shear wall (SPSW) systems is assessed by making comparisons with experimental findings Comparisons revealed that while both methods provide acceptable accuracy, they also require the generation of sophisticated computer models In this paper, two alternative methods are developed The first one is an approximate hand method based on the deep beam theory The classical deep beam theory is modified in the light of parametric studies performed on restrained thin plates under pure shear and pure bending The second one is a computer method based on the truss analogy Stiffness predictions using the two alternative methods are found to compare well with the experimental findings In addition, lateral stiffness predictions of the alternate methods are compared against the solutions provided using finite element and strip methods of analysis for a class of test structures These comparisons reveal that the developed methods provide estimates with acceptable accuracy and are simpler than the traditional analysis techniques
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TL;DR: In this paper, an integrated methodology that combines analytical and numerical techniques and deals with multidimensional lumped-parameter models of the links is proposed to improve the accuracy of stiffness models for parallel manipulators.
Abstract: The paper focuses on the accuracy improvement of stiffness models for parallel manipulators, which are employed in high-speed precision machining. It is based on the integrated methodology that combines analytical and numerical techniques and deals with multidimensional lumped-parameter models of the links. The latter replace the link flexibility by localized 6-dof virtual springs describing both translational/rotational compliance and the coupling between them. There is presented detailed accuracy analysis of the stiffness identification procedures employed in the commercial CAD systems (including statistical analysis of round-off errors, evaluating the confidence intervals for stiffness matrices). The efficiency of the developed technique is confirmed by application examples, which deal with stiffness analysis of translational parallel manipulators.
TL;DR: In this paper, a linear elastic axisymmetric finite element analysis was performed to evaluate the member stiffness, and the results obtained are compared with the results available in the literature, and wide ranges of bolt sizes, joint thicknesses and material properties were considered in the analysis to evaluate characteristic behavior of member stiffness.
Abstract: For a reliable design of bolted joints, it is necessary to evaluate the actual fraction of the external load transmitted through the bolt. The stiffness of the bolt and the member of the joint decide the fractions of external load shared by the bolt and the member. Bolt stiffness can be evaluated simply by assuming the load flow to be uniform across the thickness and the deformation is homogeneous. Then, bolt may be modeled as a tension member and the stiffness can be easily evaluated. But, the evaluation of the member stiffness is difficult because of the heterogeneous deformation. In the present work, joint materials are assumed to be isotropic and homogeneous, and linear elastic axisymmetric finite element analysis was performed to evaluate the member stiffness. Uniform displacement and uniform pressure assumptions are employed in idealizing the boundary conditions. Wide ranges of bolt sizes, joint thicknesses, and material properties are considered in the analysis to evaluate characteristic behavior of member stiffness. Empirical formulas for the member stiffness evaluation are proposed using dimensionless parameters. The results obtained are compared with the results available in the literature.
TL;DR: In this paper, the authors proposed a method for identifying arbitrary stiffness reduction in damaged reinforced concrete slab bridges under moving loads and dynamic signals measured at several points are used as response data to reflect the properties of the moving loads sensitivity.
Abstract: The method for identifying arbitrary stiffness reduction in damaged reinforced concrete slab bridges under moving loads is proposed and dynamic signals measured at several points are used as response data to reflect the properties of the moving loads sensitivity. In particular, the change in stiffness in each element before and after damage, based on the system identification method, is described and discussed by using a modified bivariate Gaussian distribution function. The proposed method in this work is more feasible than the conventional element-based damage detection method from the computational efficiency because the procedure of finite-element analysis coupled with microgenetic algorithm using six unknown parameters irrespective of the number of elements are considered. The validity of the technique is numerically verified using a set of dynamic data obtained from a simulation of the actual bridge modeled with a three-dimensional solid element. The numerical calculations show that the proposed technique is a feasible and practical method that can prove the exact location of a damaged region as well as inspect the complex distribution of deteriorated stiffness, although there is a modeling error between actual bridge results and numerical model results as well as a measurement error like uncertain noise in the response data.
01 Jan 2009
TL;DR: In this paper, a Matlab-FEM code was developed for deformation analysis of sails as a MSc final project, where sails are modelled as isotropic homogeneous membranes reinforced with cables.
Abstract: A Matlab-FEM code has been developed for deformation analysis of sails as a MSc final project. Sails are modelled as isotropic homogeneous membranes reinforced with cables. The problem, fully non-linear, is resolved by assembling the global stiffness matrix of a mesh of membrane and cable elements in the MatlabTM environment to get an N-equations N-unknowns system. The solution is found with a Quasi- Newton solver. Validation has been performed by comparing numerical results obtained from the developed code with analytical solutions of geometrically simple cases and with experimental data from tests carried out in the DINAV Ship Structures laboratory. A full Fluid Structure Interaction (FSI) analysis of a main sail has been carried out coupling the code with an aerodynamics panel code developed as another MSc final project (Vernengo, 2008). The result is in accordance with the physics of the phenomena and engineering judgment.
TL;DR: In this paper, a method is applied for the estimation of structural damage of tall slender structures using natural frequency and displacements measurements by GPS and the relationship between the variation in the global stiffness matrix (or in the stiffness of each finite element) and the change in the natural frequencies of the structure is given.
Abstract: A method is applied for the estimation of structural damage of tall slender structures using natural frequency and displacements measurements by GPS. The relationship between the variation in the global stiffness matrix (or in the stiffness of each finite element) and the change in the natural frequencies of the structure is given. In engineering practice the number of frequencies which can be derived by GPS measurement of long-period structures will be equal to one, two or three first natural frequencies. This allows us in initial studies to detect damage with frequency changes based on forward methods in which the measured frequencies are compared with the predicted analytical data. This idea, of health monitoring from possible changes to natural frequencies, or from a statement of excessive displacements is applied to the Stuttgart TV Tower.
TL;DR: In this article, an exact dynamic stiffness matrix for a generally layered composite beam on the basis of third-order shear deformation theory is derived by using the analytical solutions of the governing differential equations of the beams in free vibration.
Abstract: An exact dynamic stiffness matrix is formulated for a generally layered composite beam on the basis of third-order shear deformation theory. The Poisson effect and the couplings among the axial, torsion, and bending deformations are incorporated in the one-dimensional beam model. The dynamic stiffness matrix is derived by using the analytical solutions of the governing differential equations of the beams in free vibration. The application of the dynamic stiffness method to investigate the influences of Poisson effect, material anisotropy, slenderness, and boundary condition upon the free vibration characteristics of the laminated beams is demonstrated.
01 Jan 2009
TL;DR: In this paper, a mathematical model is presented to calculate the load distribution, single contact stiffness and meshing stiffness as well as transmission error in spur gear profile geometry, and a numerical method is employed to solve the mathematical model using a double iteration flowchart to close the problem.
Abstract: This paper firstly presents a mathematical model in order to calculate the load distribution, single contact stiffness and meshing stiffness as well as transmission error. in this way, there is no need to use finite element like methods and also the calculation time is dramatically reduced. Presented method is based on definition of a statically undetermined problem that is formulated using energy method. Some assumptions considered to convert this problem to a statically determined problem and get the mathematical models. Then a numerical method is employed in order to solve the mathematical model using a double iteration flowchart to close the problem. This model is flexible to adapt for any modification in spur gear profile geometry. Finally, this model is verified using previous works that have been utilized finite element and experimental model.Copyright © 2009 by ASME
TL;DR: In this article, a direct method based on the orthogonality constraints is proposed for updating the mass and stiffness matrices of the structure first using a single set of modal data.
Abstract: Discrepancies always exist between the dynamic properties predicted by a finite element model and those measured directly from the structure. In this study, a direct method based on the orthogonality constraints is proposed for updating the mass and stiffness matrices of the structure first using a single set of modal data. This method hinges on replacement of the modal vector of concern by the modal matrix in computing the correction matrices to solve the problem of insufficient known conditions. Such a method is then extended and applied in a consecutive manner to update the structural model for each of the first few modes that are experimentally made available. In the numerical studies, it was demonstrated that for buildings of the shear type, the natural frequencies predicted by the updated model agree well with the measured ones for those modes that are experimentally made available, while the rest modes remain basically untouched. The approach proposed herein is simple, accurate and robust, which sh...
TL;DR: In this article, the authors extended the finite volume direct average micromechanics (FVDAM) to enable the use of quadrilateral subcells, where the subcells are used to discretize the repeating unit cells first and then the average displacement and traction de-fine on the boundary of the subcell are evaluated by direct integral method.
Abstract: In this paper, we extend the finite volume direct average micromechanics to enable the use of quadrilateral subcells. To do this work, the quadrilateral subcells are used to discretize the repeating unit cells first. Then the average displacement and traction de- fined on the boundary of the subcell are evaluated by direct integral method. This con- trasts with the original formulation in which all of the subcells are rectangular. Follow- ing the discretization, the cell problem is defined by combining the directly volume- average of the subcell stress equilibrium equations with the displacement and traction continuity in a surface-average sense across the adjacent subcell faces. In order to assemble the above equations and conditions into a global equation system, the global and local number systems, which index the boundary of subcell in different manners, are employed by the extended method. Finally, the global equation system is solved and the solutions give the formulations of the microstress field and the global elastic moduli of material. The introduction of quadrilateral subcells increases the efficiency of modeling the material's microstructure and eliminates the stress concentrations at the curvilinear bimaterial corners. Herein, the advantage of the extension is presented by comparing the global moduli and local stress fields predicted by the present method with the correspond- ing results obtained from the original version. DOI: 10.1115/1.2966176 Multiscale mechanics method that evaluates the effective me- chanical properties of heterogeneous materials is becoming a very important method in present day engineering. The finite volume direct average micromechanics FVDAM for periodic multiphase materials is a recently developed micromechanics model for the response of multiphase materials with an arbitrary periodic micro- structure 1-4. The analytical framework of FVDAM is based on the homogenization theory for periodic materials cf. Kalamkarov and Kolpakov 5, but the solution of the local displacement and stress fields within the repeating unit cell utilizes the concept of local/global stiffness matrix approach. This approach discards the two-level unit cell discretization, which is used by high-fidelity generalized method of cells HFGMC6-8 and constructs the cell problems by a standard elasticity approach involving the di- rect volume-averaging of the local field equations and the satis- faction of the local continuity conditions in a surface-average sense. This simplifies the derivation of the global system of equa- tions governing the unit cell response, whose size is substantially reduced through the elimination of redundant continuity equations employed in HFGMC 1. Even though the FVDAM increases the efficiency of HFGMC, the subcells used by FVDAM to discretize the repeating unit cell are limited to rectangles Fig. 1. The approximation of curvilinear inclusions through rectangular discretization increases the re- quired number of subcells, which makes the analysis more expen- sive and also results in stress concentration at the curvilinear bi- material corners 4. In order to mitigate the negative impact of rectangular subcell mentioned above, the quadrilateral subcell dis- cretization capability was incorporated into the finite-volume theory for functional graded materials by Cavalcante et al. 9-11 and into FVDAM by Gattu 12 recently. In contrast with the parametric mapping used by Cavalcante et al., in this paper, we present another approach, which directly extends the FVDAM to enable the use of quadrilateral subcells. This is accomplished by first improving the unit cell volume discretization using quadrilat- eral subcells as the fundamental building blocks of a periodic material's microstructure Fig. 2. Then the cell problem is defined within the theoretical framework of FVDAM. The average quan- tities defined on the subcell's boundaries and the stress equilib- rium equations in average sense are evaluated by direct integral method. Finally, these equations are solved and the solution gives the microstress field and the global elastic moduli directly. Ac- cording to the character of quadrilateral subcell discretization and theoretical framework of FVDAM, the method presented in this paper is named quadrilateral finite volume direct average micro- mechanics QFVDAM. The accuracy and efficiency of the QFVDAM are demonstrated by comparing the global properties and the local stress fields of a boron/aluminum composite with the corresponding results obtained from the FVDAM.