Relevant bibliographies by topics / Variational asymptotic method

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Variational asymptotic method'

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Published: 4 June 2021
Last updated: 6 September 2023

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Journal articles on the topic "Variational asymptotic method"

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NICODEMUS, ROLF, S. GROSSMANN, and M. HOLTHAUS. "The background flow method. Part 2. Asymptotic theory of dissipation bounds." Journal of Fluid Mechanics 363 (May 25, 1998): 301–23. http://dx.doi.org/10.1017/s0022112098001177.

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We study analytically the asymptotics of the upper bound on energy dissipation for the two-dimensional plane Couette flow considered numerically in Part 1 of this work, in order to identify the mechanisms underlying the variational approach. With the help of shape functions that specify the variational profiles either in the interior or in the boundary layers, it becomes possible to quantitatively explain all numerically observed features, from the occurrence of two branches of minimizing wavenumbers to the asymptotic parameter scaling with the Reynolds number. In addition, we derive a new variational principle for the asymptotic bound on the dissipation rate. The analysis of this principle reveals that the best possible bound can only be attained if the variational profiles allow the shape of the boundary layers to change with increasing Reynolds number.
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He, Ji-Huan. "Asymptotic Methods for Solitary Solutions and Compactons." Abstract and Applied Analysis 2012 (2012): 1–130. http://dx.doi.org/10.1155/2012/916793.

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This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this paper are first appeared.
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Sutyrin, V. G. "Derivation of Plate Theory Accounting Asymptotically Correct Shear Deformation." Journal of Applied Mechanics 64, no. 4 (1997): 905–15. http://dx.doi.org/10.1115/1.2788998.

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The focus of this paper is the development of linear, asymptotically correct theories for inhomogeneous orthotropic plates, for example, laminated plates with orthotropic laminae. It is noted that the method used can be easily extended to develop nonlinear theories for plates with generally anisotropic inhomogeneity. The development, based on variational-asymptotic method, begins with three-dimensional elasticity and mathematically splits the analysis into two separate problems: a one-dimensional through-the-thickness analysis and a two-dimensional “plate” analysis. The through-the-thickness analysis provides elastic constants for use in the plate theory and approximate closed-form recovering relations for all truly three-dimensional displacements, stresses, and strains expressed in terms of plate variables. In general, the specific type of plate theory that results from variational-asymptotic method is determined by the method itself. However, the procedure does not determine the plate theory uniquely, and one may use the freedom appeared to simplify the plate theory as much as possible. The simplest and the most suitable for engineering purposes plate theory would be a “Reissner-like” plate theory, also called first-order shear deformation theory. However, it is shown that construction of an asymptotically correct Reissner-like theory for laminated plates is not possible in general. A new point of view on the variational-asymptotic method is presented, leading to an optimization procedure that permits a derived theory to be as close to asymptotical correctness as possible while it is a Reissner-like. This uniquely determines the plate theory. Numerical results from such an optimum Reissner-like theory are presented. These results include comparisons of plate displacement as well as of three-dimensional field variables and are the best of all extant Reissner-like theories. Indeed, they even surpass results from theories that carry many more generalized displacement variables. Although the derivation presented herein is inspired by, and completely equivalent to, the well-known variational-asymptotic method, the new procedure looks different. In fact, one does not have to be familiar with the variational-asymptotic method in order to follow the present derivation.
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Gottwald, Georg A., and Marcel Oliver. "Slow dynamics via degenerate variational asymptotics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2170 (2014): 20140460. http://dx.doi.org/10.1098/rspa.2014.0460.

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We introduce the method of degenerate variational asymptotics for a class of singularly perturbed ordinary differential equations in the limit of strong gyroscopic forces. Such systems exhibit dynamics on two separate time scales. We derive approximate equations for the slow motion to arbitrary order through an asymptotic expansion of the Lagrangian in suitably transformed coordinates. We prove that the necessary near-identity change of variables can always be constructed and that solutions of the slow limit equations shadow solutions of the full parent model at the expected order over a finite interval of time.
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HE, JI-HUAN. "SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS." International Journal of Modern Physics B 20, no. 10 (2006): 1141–99. http://dx.doi.org/10.1142/s0217979206033796.

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This paper features a survey of some recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the obtained approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to overcome the shortcomings. In this paper the following categories of asymptotic methods are emphasized: (1) variational approaches, (2) parameter-expanding methods, (3) parameterized perturbation method, (4) homotopy perturbation method (5) iteration perturbation method, and ancient Chinese methods. The emphasis of this article is put mainly on the developments in this field in China so the references, therefore, are not exhaustive.
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YARMUKHAMEDOV, R., та M. K. UBAYDULLAEVA. "ON ASYMPTOTICS OF THREE-BODY BOUND STATE RADIAL WAVE FUNCTIONS OF HALO NUCLEI NEAR THE HYPERANGLE φ~0 AND φ~π/2 IN THE CONFIGURATION SPACE AND THREE-BODY ASYMPTOTIC NORMALIZATION FACTORS FOR 6He NUCLEUS IN THE (n+n+α)-CHANNEL". International Journal of Modern Physics E 18, № 07 (2009): 1561–85. http://dx.doi.org/10.1142/s0218301309013701.

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Asymptotic expressions for the bound state radial partial wave functions of three-body (nnc) halo nuclei with two loosely bound valence neutrons (n) are obtained in explicit form, when the relative distance between two neutrons (r) tends to infinity and the relative distance between the center of mass of core (c) and two neutrons (ρ) is too small or vice versa. These asymptotic expressions contain a factor that can strongly influence the asymptotic values of the three-body radial wave function in the vicinity of the hyperangle of φ~0 except 0 (r→∞ and ρ is too small except 0) or φ~π/2 except π/2 (ρ→∞ and r is too small except 0) in the configuration space. The derived asymptotic forms are applied to the analysis of the asymptotic behavior of the three-body (nnα) wave function for 6He nucleus obtained by other authors on the basis of multicluster stochastic variational method using the two forms of the αN-potential. The ranges of r (or ρ) from the asymptotical regions are determined for which the agreement between the calculated wave function and the asymptotics formulae is reached. Information about the values of the three-body asymptotic normalization factors is extracted.
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Baranwal, Vipul K., Ram K. Pandey, and Om P. Singh. "Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations." International Scholarly Research Notices 2014 (October 15, 2014): 1–12. http://dx.doi.org/10.1155/2014/847419.

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We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ0,γ1,γ2,… and auxiliary functions H0(x),H1(x),H2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.
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Sachdeva, Chirag, and Srikant S. Padhee. "Analysis of Bidirectionally Graded Cylindrical Beams Using Variational Asymptotic Method." AIAA Journal 57, no. 10 (2019): 4169–81. http://dx.doi.org/10.2514/1.j057562.

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Shibata, Tetsutaro. "Variational method for precise asymptotic formulas for nonlinear eigenvalue problems." Results in Mathematics 46, no. 1-2 (2004): 130–45. http://dx.doi.org/10.1007/bf03322876.

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Li, Xi, and Da-ming Yuan. "Asymptotic approximation method for elliptic variational inequality of first kind." Applied Mathematics and Mechanics 35, no. 3 (2014): 381–90. http://dx.doi.org/10.1007/s10483-014-1798-x.

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Dissertations / Theses on the topic "Variational asymptotic method"

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Lee, Chang-Yong. "Dynamic Variational Asymptotic Procedure for Laminated Composite Shells." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/16265.

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Unlike published shell theories, the main two parts of this thesis are devoted to the asymptotic construction of a refined theory for composite laminated shells valid over a wide range of frequencies and wavelengths. The resulting theory is applicable to shells each layer of which is made of materials with monoclinic symmetry. It enables one to analyze shell dynamic responses within both long-wavelength, low- and high-frequency vibration regimes. It also leads to energy functionals that are both positive definiteness and sufficient simplicity for all wavelengths. This whole procedure was first performed analytically. From the insight gained from the procedure, a finite element version of the analysis was then developed; and a corresponding computer program, DVAPAS, was developed. DVAPAS can obtain the generalized 2-D constitutive law and recover accurately the 3-D results for stress and strain in composite shells. Some independent works will be needed to develop the corresponding 2-D surface analysis associated with the present theory and to continue towards full verification and validation of the present process by comparison with available published works.
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Tang, Tian. "Variational Asymptotic Micromechanics Modeling of Composite Materials." DigitalCommons@USU, 2008. https://digitalcommons.usu.edu/etd/72.

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The issue of accurately determining the effective properties of composite materials has received the attention of numerous researchers in the last few decades and continues to be in the forefront of material research. Micromechanics models have been proven to be very useful tools for design and analysis of composite materials. In the present work, a versatile micromechanics modeling framework, namely, the Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH), has been invented and various micromechancis models have been constructed in light of this novel framework. Considering the periodicity as a small parameter, we can formulate the variational statements of the unit cell through an asymptotic expansion of the energy functional. It is shown that the governing differential equations and periodic boundary conditions of mathematical homogenization theories (MHT) can be reproduced from this variational statement. Finally, we employed the finite element method to solve the numerical solution of the constrained minimization problem. If the local fields within the unit cell are of interest, the proposed models can also accurately recover those fields based on the global behavior. In comparison to other existing models, the advantages of VAMUCH are: (1) it invokes only two essential assumptions within the concept of micromechanics for heterogeneous material with identifiable unit cells; (2) it has an inherent variational nature and its numerical implementation is shown to be straightforward; (3) it calculates the different material properties in different directions simultaneously, which is more efficient than those approaches requiring multiple runs under different loading conditions; and (4) it calculates the effective properties and the local fields directly with the same accuracy as the fluctuation functions. No postprocessing calculations such as stress averaging and strain averaging are needed. The present theory is implemented in the computer program VAMUCH, a versatile engineering code for the homogenization of heterogeneous materials. This new micromechanics modeling approach has been successfully applied to predict the effective properties of composite materials including elastic properties, coefficients of thermal expansion, and specific heat and the effective properties of piezoelectric and electro-magneto-elastic composites. This approach has also been extended to the prediction of the nonlinear response of multiphase composites. Numerous examples have been utilized to clearly demonstrate its application and accuracy as a general-purpose micromechanical analysis tool.
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Kovvali, Ravi Kumar. "A nonlinear theory of Cosserat elastic plates using the variational-asymptotic method." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/54342.

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One of the most important branches of applied mechanics is the theory of plates - defined to be plane structural elements whose thickness is very small when compared to the two planar dimensions. There is an abundance of plate theories in the literature modeling classical elastic solids that fit this description. Recently, however, there has been a steady growth of interest in modeling materials with microstructures that exhibit length-scale dependent behavior, generally known as Cosserat elastic materials. Concurrently, there has also been an increased interest in the construction of reduced dimensional models of such materials owing to advantages like reduced computational effort and a simpler, yet elegant, resulting mathematical formulation. The objective of this work is the formulation and implementation of a theory of elastic plates with microstructure. The mathematical underpinning of the approach used is the Variational Asymptotic Method (VAM), a powerful tool used to construct asymptotically correct plate models. Unlike existing Cosserat plate models in the literature, the VAM allows for a plate formulation that is free of a priori assumptions regarding the kinematics. The result is a systematic derivation of the two-dimensional constitutive relations and a set of geometrically-exact, fully intrinsic equations gov- erning the motion of a plate. An important consequence is the extraction of the drilling degree of freedom and the associated stiffness. Finally, a Galerkin approach for the solution of the fully-intrinsic formulation will be developed for a Cosserat sur- face analysis which will also be compatible with more traditional plate solvers based on the classical theory of elasticity. Results and validation are presented from linear static and dynamic analyses, along with a discussion on some challenges and solution techniques for nonlinear problems.One of the most important branches of applied mechanics is the theory of plates - defined to be plane structural elements whose thickness is very small when compared to the two planar dimensions. There is an abundance of plate theories in the literature modeling classical elastic solids that fit this description. Recently, however, there has been a steady growth of interest in modeling materials with microstructures that exhibit length-scale dependent behavior, generally known as Cosserat elastic materials. Concurrently, there has also been an increased interest in the construction of reduced dimensional models of such materials owing to advantages like reduced computational effort and a simpler, yet elegant, resulting mathematical formulation. The objective of this work is the formulation and implementation of a theory of elastic plates with microstructure. The mathematical underpinning of the approach used is the Variational Asymptotic Method (VAM), a powerful tool used to construct asymptotically correct plate models. Unlike existing Cosserat plate models in the literature, the VAM allows for a plate formulation that is free of a priori assumptions regarding the kinematics. The result is a systematic derivation of the two-dimensional constitutive relations and a set of geometrically-exact, fully intrinsic equations gov- erning the motion of a plate. An important consequence is the extraction of the drilling degree of freedom and the associated stiffness. Finally, a Galerkin approach for the solution of the fully-intrinsic formulation will be developed for a Cosserat sur- face analysis which will also be compatible with more traditional plate solvers based on the classical theory of elasticity. Results and validation are presented from linear static and dynamic analyses, along with a discussion on some challenges and solution techniques for nonlinear problems.
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Rajagopal, Anurag. "Advancements in rotor blade cross-sectional analysis using the variational-asymptotic method." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51877.

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Rotor (helicopter/wind turbine) blades are typically slender structures that can be modeled as beams. Beam modeling, however, involves a substantial mathematical formulation that ultimately helps save computational costs. A beam theory for rotor blades must account for (i) initial twist and/or curvature, (ii) inclusion of composite materials, (iii) large displacements and rotations; and be capable of offering significant computational savings compared to a non-linear 3D FEA (Finite Element Analysis). The mathematical foundation of the current effort is the Variational Asymptotic Method (VAM), which is used to rigorously reduce the 3D problem into a 1D or beam problem, i.e., perform a cross-sectional analysis, without any ad hoc assumptions regarding the deformation. Since its inception, the VAM based cross-sectional analysis problem has been in a constant state of flux to expand its horizons and increase its potency; and this is precisely the target at which the objectives of this work are aimed. The problems addressed are the stress-strain-displacement recovery for spanwise non-uniform beams, analytical verification studies for the initial curvature effect, higher fidelity stress-strain-displacement recovery, oblique cross-sectional analysis, modeling of thin-walled beams considering the interaction of small parameters and the analysis of plates of variable thickness. The following are the chief conclusions that can be drawn from this work: 1. In accurately determining the stress, strain and displacement of a spanwise non-uniform beam, an analysis which accounts for the tilting of the normal and the subsequent modification of the stress-traction boundary conditions is required. 2. Asymptotic expansion of the metric tensor of the undeformed state and its powers are needed to capture the stiffnesses of curved beams in tune with elasticity theory. Further improvements in the stiffness matrix can be achieved by a partial transformation to the Generalized Timoshenko theory. 3. For the planar deformation of curved laminated strip-beams, closed-form analytical expressions can be generated for the stiffness matrix and recovery; further certain beam stiffnesses can be extracted not only by a direct 3D to 1D dimensional reduction, but a sequential dimensional reduction, the intermediate being a plate theory. 4. Evaluation of the second-order warping allows for a higher fidelity extraction of stress, strain and displacement with negligible additional computational costs. 5. The definition of a cross section has been expanded to include surfaces which need not be perpendicular to the reference line. 6. Analysis of thin-walled rotor blade segments using asymptotic methods should consider a small parameter associated with the wall thickness; further the analysis procedure can be initiated from a laminated shell theory instead of 3D. 7. Structural analysis of plates of variable thickness involves an 8×8 plate stiffness matrix and 3D recovery which explicitly depend on the parameters describing the thickness, in contrast to the simplistic and erroneous approach of replacing the thickness by its variation.
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Wang, Qi. "Asymptotic Multiphysics Modeling of Composite Beams." DigitalCommons@USU, 2011. https://digitalcommons.usu.edu/etd/1066.

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A series of composite beam models are constructed for efficient high-fidelity beam analysis based on the variational-asymptotic method (VAM). Without invoking any a priori kinematic assumptions, the original three-dimensional, geometrically nonlinear beam problem is rigorously split into a two-dimensional cross-sectional analysis and a one-dimensional global beam analysis, taking advantage of the geometric small parameter that is an inherent property of the structure. The thermal problem of composite beams is studied first. According to the quasisteady theory of thermoelasticity, two beam models are proposed: one for heat conduction analysis and the other for thermoelastic analysis. For heat conduction analysis, two different types of thermal loads are modeled: with and without prescribed temperatures over the crosssections. Then a thermoelastic beam model is constructed under the previously solved thermal field. This model is also extended for composite materials, which removed the restriction on temperature variations and added the dependence of material properties with respect to temperature based on Kovalenoko’s small-strain thermoelasticity theory. Next the VAM is applied to model the multiphysics behavior of beam structure. A multiphysics beam model is proposed to capture the piezoelectric, piezomagnetic, pyroelectric, pyromagnetic, and hygrothermal effects. For the zeroth-order approximation, the classical models are in the form of Euler-Bernoulli beam theory. In the refined theory, generalized Timoshenko models have been developed, including two transverse shear strain measures. In order to avoid ill-conditioned matrices, a scaling method for multiphysics modeling is also presented. Three-dimensional field quantities are recovered from the one-dimensional variables obtained from the global beam analysis. A number of numerical examples of different beams are given to demonstrate the application and accuracy of the present theory. Excellent agreements between the results obtained by the current models and those obtained by three-dimensional finite element analysis, analytical solutions, and those available in the literature can be observed for all the cross-sectional variables. The present beam theory has been implemented into the computer program VABS (Variational Asymptotic Beam Sectional Analysis).
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Teng, Chong. "Variational Asymptotic Method for Unit Cell Homogenization of Thermomechanical Behavior of Composite Materials." DigitalCommons@USU, 2013. https://digitalcommons.usu.edu/etd/2048.

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To seek better material behaviors, the research of material properties has been mas- sively carried out in both industrial and academic fields throughout the twentieth century. Composite materials are known for their abilities of combining constituent materials in or- der to fulfill the desirable overall material performance. One of the advantages of composite materials is the adjustment between stiffness and lightness of materials in order to meet the needs of various engineering designs. Even though the finite element analysis is mature, composites are heterogeneous in nature and can present difficulties at the structural level with the acceptable computational time. A way of simplifying such problems is to find a way to connect structural analysis with corresponding analysis of representative microstructure of the material, which is normally called micromechanics modeling or homogenization.Generally speaking, the goal of homogenization is to predict a precise material behavior by taking into account the information stored in both microscopic and macroscopic levels of the composites. Of special concern to researchers and engineers is the thermomechanical behavior of composite materials since thermal effect is almost everywhere in real practical cases of engineering. In aerospace engineering, the thermomechanical behaviors of compos- ites are even more important since flight under high speed usually produces a large amount of heat which will cause very high thermal-related deformation and stress.In this dissertation, the thermomechanical behavior of composites will be studied based on the variational asymptotic method for unit cell homogenization (VAMUCH) which was recently developed as an efficient and accurate micromechanics modeling tool. The theories and equations within the code are based on the variational asymptotic method invented by Prof. Berdichevsky. For problems involving small parameters, the traditional asymptotic method is often applied by solving a system of differential equations while the variational asymptotic method is using a variational statement that only solves one functional of such problems where the traditional asymptotic method may apply.First, we relax the assumption made by traditional linear thermoelasticity that not only a small overall strain is assumed to be small but also the temperature variation. Of course, in this case we need to add temperature dependent material properties to VAMUCH so that the secant material properties can be calculated. Then, we consider the temperature field to be point-wise different within the microstructure; a micromechanics model with nonuniformly distributed temperature field will be addressed. Finally, the internal and external loads induced energies are considered in order to handle real engineering structures under their working conditions.
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Ye, Zheng. "Enhance Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH) for Real Engineering Structures and Materials." DigitalCommons@USU, 2013. https://digitalcommons.usu.edu/etd/1732.

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Modern technologies require the materials with combinations of properties that can not be met by conventional single phase materials. This requirement leads to the development of composite materials or other materials with engineered microstructures, such as polymer composites and nanotube. Though the well-established finite element analysis (FEA) has the ability to analyze a small portion of such material, for the whole structure, the total degrees of freedom of a finite element model can easily exceed the bearable time in analysis or the capability of the best mainstream computers. To reduce the total degrees of freedom and save the computational efforts, an efficient way is to use a simpler and coarser mesh at the structure level with the micro level complexities captured by a homogenization method. Throughout the dissertation, the homogenization is carried on by variational asymptotic method which has been developed recently as the Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH). This methodology is also expandable to the structure analysis as long as a representative structural element (RSE) can be obtained from structure. In the present research, the following problems are handled: (1) Maximizing the flexibility of choosing a RSE; (2) Bounding the effective properties of a random RSE; (3) Obtaining the equivalent plate stiffnesses for a corrugated plate from a RSE; (4) Extending the shell element of relative degree of freedom to analyze thin-walled RSE. These problems covered some important topics in homogenization theory. Firstly, the rules need to be followed when choosing a unit cell from a structure that can be homogenized. Secondly, for a randomly packed structure, the efficient way to predict effective material properties is to predict their bounds. Then, the composite material homogenization and the structural homogenization can be unied from a mathematical point of view, thus the repeating structure can be always simplified by the homogenization method. Lastly, the efficiency of analyzing thin-walled structures has been enhanced by the new type of shell element. In this research, the first two topics have been solved numerically through the finite element method under the framework of VAMUCH. The third one has been solved both analytically and numerically, and in the last, a new type of element has been implemented in VAMUCH to adapt the characteristics of a thin-walled problem. Numerous examples have demonstrated VAMUCH application and accuracy as a general-purpose analysis tool.
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Song, Huimin. "Rigorous joining of advanced reduced-dimensional beam models to 3D finite element models." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/33901.

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This dissertation developed a method that can accurately and efficiently capture the response of a structure by rigorous combination of a reduced-dimensional beam finite element model with a model based on full two-dimensional (2D) or three-dimensional (3D) finite elements. As a proof of concept, a joint 2D-beam approach is studied for planar-inplane deformation of strip-beams. This approach is developed for obtaining understanding needed to do the joint 3D-beam model. A Matlab code is developed to solve achieve this 2D-beam approach. For joint 2D-beam approach, the static response of a basic 2D-beam model is studied. The whole beam structure is divided into two parts. The root part where the boundary condition is applied is constructed as a 2D model. The free end part is constructed as a beam model. To assemble the two different dimensional model, a transformation matrix is used to achieve deflection continuity or load continuity at the interface. After the transformation matrix from deflection continuity or from load continuity is obtained, the 2D part and the beam part can be assembled together and solved as one linear system. For a joint 3D-beam approach, the static and dynamic response of a basic 3D-beam model is studied. A Fortran program is developed to achieve this 3D-beam approach. For the uniform beam constrained at the root end, similar to the joint 2D-beam analysis, the whole beam structure is divided into two parts. The root part where the boundary condition is applied is constructed as a 3D model. The free end part is constructed as a beam model. To assemble the two different dimensional models, the approach of load continuity at the interface is used to combine the 3D model with beam model. The load continuity at the interface is achieved by stress recovery using the variational-asymptotic method. The beam properties and warping functions required for stress recovery are obtained from VABS constitutive analysis. After the transformation matrix from load continuity is obtained, the 3D part and the beam part can be assembled together and solved as one linear system. For a non-uniform beam example, the whole structure is divided into several parts, where the root end and the non-uniform parts are constructed as 3D models and the uniform parts are constructed as beams. At all the interfaces, the load continuity is used to connect 3D model with beam model. Stress recovery using the variational-asymptotic method is used to achieve the load continuity at all interfaces. For each interface, there is a transformation matrix from load continuity. After we have all the transformation matrices, the 3D parts and the beam parts are assembled together and solved as one linear system.
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Chakravarty, Uttam Kumar. "Section builder: a finite element tool for analysis and design of composite." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/22640.

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Thesis (Ph. D.)--Aerospace Engineering, Georgia Institute of Technology, 2008.<br>Committee Chair: Bauchau, Olivier; Committee Member: Craig, James; Committee Member: Hodges, Dewey; Committee Member: Mahfuz, Hassan; Committee Member: Volovoi, Vitali.
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Lee, Bok W. "Application of variational-asymptotical method to laminated composite plates." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/20695.

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Books on the topic "Variational asymptotic method"

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Kogut, Peter I. Optimal control problems for partial differential equations on reticulated domains: Approximation and asymptotic analysis. Birkhäuser, 2011.

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1966-, Pérez Joaquín, and Galvez José A. 1972-, eds. Geometric analysis: Partial differential equations and surfaces : UIMP-RSME Santaló Summer School geometric analysis, June 28-July 2, 2010, University of Granada, Granada, Spain. American Mathematical Society, 2012.

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Lewicka, Marta. Calculus of Variations on Thin Prestressed Films: Asymptotic Methods in Elasticity. Springer International Publishing AG, 2023.

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Kogut, Peter I., and Günter R. Leugering. Optimal Control Problems for Partial Differential Equations on Reticulated Domains: Approximation and Asymptotic Analysis. Birkhäuser, 2011.

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Optimal Control Problems for Partial Differential Equations on Reticulated Domains: Approximation and Asymptotic Analysis. Birkhäuser Boston, 2011.

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Book chapters on the topic "Variational asymptotic method"

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Novotny, Antonio André, Jan Sokołowski, and Antoni Żochowski. "Asymptotic Analysis of Variational Inequalities." In Applications of the Topological Derivative Method. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-05432-8_9.

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Yu, Wenbin, and Tian Tang. "Variational Asymptotic Method for Unit Cell Homogenization." In Solid Mechanics and Its Applications. Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-3467-0_9.

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Burela, Ramesh Gupta, and Dineshkumar Harursampath. "Asymptotically-Accurate Nonlinear Hyperelastic Shell Constitutive Model Using Variational Asymptotic Method." In Advanced Structured Materials. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17747-8_9.

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Ghorashi, Mehrdaad. "Review of the Variational Asymptotic Method and the Intrinsic Equations of a Beam." In Statics and Rotational Dynamics of Composite Beams. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-14959-2_2.

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Zaman, Izzuddin, Nurul Jannah Mohammad, Bukhari Manshoor, and Amir Khalid. "Micromechanical Modeling of Glass Filled Epoxy Using the Variational Asymptotic Method for Unit Cell Homogenization." In Proceedings of the 2nd Energy Security and Chemical Engineering Congress. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-4425-3_24.

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Salunkhe, Santosh B., B. T. Gadade, V. S. Pawar, and P. J. Guruprasad. "A Variational Asymptotic Method Based Free Vibration Analysis of a Thin Pretwisted and Delaminated Anisotropic Strip." In Techno-Societal 2018. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16962-6_72.

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Pesce, C. P., and J. A. P. Aranha. "Asymptotic and Variational Methods Applied to the Evaluation of Wave Drift Forces." In Advances in Berthing and Mooring of Ships and Offshore Structures. Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-1407-0_23.

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Lindenstrauss, Joram, David Preiss, and Tiˇser Jaroslav. "Asymptotic Fr echet ´Differentiability." In Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179). Princeton University Press, 2012. http://dx.doi.org/10.23943/princeton/9780691153551.003.0015.

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This chapter presents the current development of the first, unpublished proof of existence of points Fréchet differentiability of Lipschitz mappings to two-dimensional spaces. For functions into higher dimensional spaces the method does not lead to a point of Gâteaux differentiability but constructs points of asymptotic Fréchet differentiability. The proof uses perturbations that are not additive, rather than the variational approach, but still provides (asymptotic) Fréchet derivatives in every slice of Gâteaux derivatives. However, it cannot be used to prove existence of points of Fréchet differentiability of Lipschitz mappings of Hilbert spaces to three-dimensional spaces. The results are negative in the sense that an appropriate version of the multidimensional mean value estimate holds.
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Tadie. "Steady vortex rings in an ideal fluid: asymptotics for variational solutions." In Integral methods in science and engineering. Chapman and Hall/CRC, 2020. http://dx.doi.org/10.1201/9780367812027-36.

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Aïıt-Sahalia, Yacine, and Jean Jacod. "With Jumps: An Introduction to Power Variations." In High-Frequency Financial Econometrics. Princeton University Press, 2014. http://dx.doi.org/10.23943/princeton/9780691161433.003.0004.

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This chapter studies the simplest possible process having both a non-trivial continuous part and jumps. It starts with the asymptotic behavior of power variations when the model is nonparametric, that is, without specifying the law of the jumps. This is done in the same spirit as in Chapter 3: the ideas for the proofs are explained in detail, but technicalities are omitted. Then, it considers the use of these variations in a parametric estimation setting based on the generalized method of moments. There, it considers the ability of certain moment functions, corresponding to power variations, to achieve identification of the parameters of the model and the resulting rate of convergence. It shows that the general nonparametric results have a parametric counterpart in terms of which values of the power p are better able to identify parameters from either the continuous or jump part of the model.
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Conference papers on the topic "Variational asymptotic method"

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Agrawal, Shashank, and Dineshkumar Harursampath. "Modeling of piezocomposites using variational asymptotic method." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912585.

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Yu, Wenbin. "A Variational-Asymptotic Cell Method for Periodically Heterogeneous Materials." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79611.

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A new cell method, variational-asymptotic cell method (VACM), is developed to homogenize periodically heterogenous anisotropic materials based on the variational asymptotic method. The variational asymptotic method is a mathematical technique to synthesize both merits of variational methods and asymptotic methods by carrying out the asymptotic expansion of the functional governing the physical problem. Taking advantage of the small parameter (the periodicity in this case) inherent in the heterogenous solids, we can use the variational asymptotic method to systematically obtain the effective material properties. The main advantages of VACM are that: a) it does not rely on ad hoc assumptions; b) it has the same rigor as mathematical homogenization theories; c) its numerical implementation is straightforward because of its variational nature; d) it can calculate different material properties in different directions simultaneously without multiple analyses. To illustrate the application of VACM, a binary composite with two orthotropic layers are studied analytically, and a closed-form solution is given for effective stiffness matrix and the corresponding effective engineering constants. It is shown that VACM can reproduce the results of a mathematical homogenization theory.
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Roy, Sitikantha, and Wenbin Yu. "A Variational-Asymptotic Theory of Smart Slender Structures." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79587.

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The goal of the present work is to develop an efficient simulation tool with high-fidelity to help the engineers design and analyze smart slender structures with embedded piezoelectric materials. Actuation and sensing capabilities of piezoelectric material embedded in smart beam including geometric nonlinearity will be explored. The dimensional reduction process has been carried out using the powerful Variational Asymptotic Method. Starting from the exact three-dimensional electric-mechanically coupled enthalpy functional, the asymptotical analysis is done on the functional itself with respect to the naturally occurring small parameters. The original three-dimensional electric-mechanical problem of the slender structure is decomposed into two separate problems: a two-dimensional analysis over the cross section and a one-dimensional analysis over the beam reference line. The coupled cross-sectional analysis is being implemented in VABS, a versatile cross-sectional analysis code.
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Kobayashi, Marcelo, and Melike Nikbay. "On a Fourier Spectral Variational Asymptotic Method for Cellular Composite Structures." In 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-1543.

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Tang, Tian, and Wenbin Yu. "A Multiphysics Micromechanics Model of Smart Materials Using the Variational Asymptotic Method." In ASME 2008 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2008. http://dx.doi.org/10.1115/smasis2008-366.

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The primary objective of the present paper is to develop a micromechanics model for the prediction of the effective properties and the distribution of local fields of smart materials which are responsive to fully coupled electric, magnetic, thermal and mechanical fields. This work is based on the framework of the variational asymptotic method for unit cell homogenization (VAMUCH), a recently developed micromechanics modeling scheme. For practicle use of this theory, we implement this new model using the finite element method into the computer program VAMUCH. For validation, several examples will be presented in the full paper to compare with existing models and demonstrate the application and advantages of the new model.
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Zhang, Liang, and Wenbin Yu. "A Variational Asymptotic Method for Unit Cell Homogenization of Elastoplastic Heterogeneous Materials." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-89058.

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The variational asymptotic method for unit cell homogenization (VAMUCH) is a unified micromechanical numerical method that is able to predict the effective properties of heterogeneous materials and to recover the microscopic stress/strain field. The objective of this paper is to incorporate elastoplastic material behaviors into the VAMUCH to predict the nonlinear macroscopic/microscopic response of elastoplastic heterogeneous materials. The constituents are assumed to exhibit various behaviors including elastic/plastic anisotropy, isotropic/kinematic hardening, and plastic non-normality. The constitutive relations for the constituents are derived and implemented into the theory of VAMUCH. This theory is implemented using the finite element method, and an engineering code, VAMUCH, is developed for the micromechanical analysiso of unit cells. The applicability, power, and accuracy of the theory and code of VAMUCH are validated using several examples including predicting the initial and subsequent yield surfaces, stress-strain curves, and stress-strain hysteresis loops of fiber reinforced composites. The VAMUCH code is also ready to be implemented into many more sophisticated user-defined material models.
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Zhang, Liang, and Wenbin Yu. "A Variational Asymptotic Method for Unit Cell Homogenization of Hyperelastic Heterogeneous Materials." In 55th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. American Institute of Aeronautics and Astronautics, 2014. http://dx.doi.org/10.2514/6.2014-1335.

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Zhang, Liang, and Wenbin Yu. "A Variational Asymptotic Method for Unit Cell Homogenization of Elasto-Viscoplastic Heterogeneous Materials." In 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-1958.

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Ameen, Maqsood M., and Dineshkumar Harursampath. "Analysis of transverse shear strains in pre-twisted thick beams using variational asymptotic method." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912586.

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Yu, Emily, and Lih-Sheng Turng. "Prediction of Mechanical Properties of Microcellular Plastics Using the Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH) Method." In ASME 2013 International Manufacturing Science and Engineering Conference collocated with the 41st North American Manufacturing Research Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/msec2013-1254.

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This work presents the application of the micromechanical variational asymptotic method for unit cell homogenization (VAMUCH) with a three-dimensional unit cell (UC) structure and a coupled, macroscale finite element analysis for analyzing and predicting the effective elastic properties of microcellular injection molded plastics. A series of injection molded plastic samples — which included polylactic acid (PLA), polypropylene (PP), polystyrene (PS), and thermoplastic polyurethane (TPU) — with microcellular foamed structures were produced and their mechanical properties were compared with predicted values. The results showed that for most material samples, the numerical prediction was in fairly good agreement with experimental results, which demonstrates the applicability and reliability of VAMUCH in analyzing the mechanical properties of porous materials. The study also found that material characteristics such as brittleness or ductility could influence the predicted results and that the VAMUCH prediction could be improved when the UC structure was more representative of the real composition.
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Reports on the topic "Variational asymptotic method"

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Chronopoulos, Ilias, Katerina Chrysikou, George Kapetanios, James Mitchell, and Aristeidis Raftapostolos. Deep Neural Network Estimation in Panel Data Models. Federal Reserve Bank of Cleveland, 2023. http://dx.doi.org/10.26509/frbc-wp-202315.

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In this paper we study neural networks and their approximating power in panel data models. We provide asymptotic guarantees on deep feed-forward neural network estimation of the conditional mean, building on the work of Farrell et al. (2021), and explore latent patterns in the cross-section. We use the proposed estimators to forecast the progression of new COVID-19 cases across the G7 countries during the pandemic. We find significant forecasting gains over both linear panel and nonlinear time-series models. Containment or lockdown policies, as instigated at the national level by governments, are found to have out-of-sample predictive power for new COVID-19 cases. We illustrate how the use of partial derivatives can help open the "black box" of neural networks and facilitate semi-structural analysis: school and workplace closures are found to have been effective policies at restricting the progression of the pandemic across the G7 countries. But our methods illustrate significant heterogeneity and time variation in the effectiveness of specific containment policies.
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Yogev, David, Ricardo Rosenbusch, Sharon Levisohn, and Eitan Rapoport. Molecular Pathogenesis of Mycoplasma bovis and Mycoplasma agalactiae and its Application in Diagnosis and Control. United States Department of Agriculture, 2000. http://dx.doi.org/10.32747/2000.7573073.bard.

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Mycoplasma bovis and M. agalactiae are two phylogenetically related mycoplasmas which cause economically significant diseases in their respective bovine or small ruminant hosts. These organisms cause persistent asymptomatic infections that can result in severe outbreaks upon introduction of carrier animals into susceptible herds. Little is known about the mechanisms underlying mycoplasma-host interaction, variation in virulence, or of the factors enabling avoidance of the host immune system. In recent years it has become apparent that the ability of pathogenic microorganisms to rapidly alter surface antigenic structures and to fine tune their antigenicity, a phenomena called antigenic variation, is one of the most effective strategies used to escape immune destruction and to establish chronic infections. Our discovery of a novel genetic system, mediating antigenic variation in M. bovis (vsp) as well as in M. agalactiae (avg) served as a starting point for our proposal which included the following objectives: (i) Molecular and functional characterization of the variable surface lipoproteins (Vsp) system of M. bovis and comparison with the Vsp-counterpart in M. agalactiae (ii) Determination of the role of Vsp proteins in the survival of M. bovis when confronted by host defense factors, (iii) Assessment of Vsp-based genetic and antigenic typing of M. bovis and M. agalactiae for epidemiology of infection and (iv) Improvement of diagnostic tests for M. bovis and M. agalactiae based on the vsp-and vsp-analogous systems. We have carried out an extensive molecular characterization of the vsp system and unravelled the precise molecular mechanism responsible for the generation of surface antigenic variation in M. bovis. Our data clearly demonstrated that the two pathogenic mycoplasma species possess large gene families encoding variable lipoprotein antigens that apparently play an important role in immune evasion and in pathogen-host interaction during infection. Phase variable production of these antigens was found to be mediated by a novel molecular mechanism utilizing double site-specific DNA inversions via an intermediate vsp configuration. Studies in model systems indicate that phase variation of VspA is relevant in interaction between M. bovis and macrophages or monocytes, a crucial stage in pathogenesis. Using an ELISA test with captured VspA as an antigen, phase variation was shown to occur in vivo and under field conditions. Genomic rearrangements in the avg gene family of M. agalactiae were shown to occur in vivo and may well have a role in evasion of host defences and establishment of chronic infection. An epidemiological study indicated that patterns of vsp-related antigenic variation diverge rapidly in an M. bovis infected herd. Marked divergence was also found with avg-based genomic typing of M. agalactiae in chronically infected sheep. However, avg-genomic fingerprints were found to be relatively homogeneous in different animals during acute stages of an outbreak of Contagious Agalactiae, and differ between unrelated outbreaks. These data support the concept of vsp-based genomic typing but indicate the necessity for further refinement of the methodology. The molecular knowledge on these surface antigens and their encoding genes provides the basis for generating specific recombinant tools and serological methods for serodiagnosis and epidemiological purposes. Utilization of these methods in the field may allow differentiating acutely infected herds from chronic herds and disease-free herds. In addition the highly immunogenic nature of these lipoproteins may facilitate the design of protective vaccine against mycoplasma infections.
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Freeman, Stanley, and Daniel Legard. Epidemiology and Etiology of Colletotrichum Species Causing Strawberry Diseases. United States Department of Agriculture, 2001. http://dx.doi.org/10.32747/2001.7695845.bard.

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Diseases caused by Colletotrichum spp. are one of the most important limitations on international strawberry production, affecting all vegetative and fruiting parts of the plant. From 1995 to 1997, C. acutatum infections reached epidemic levels in Israeli strawberry nurseries, causing extensive loss of transplants in fruit-bearing fields and additional reductions in yield. Although C. acutatum also occurs on strawberry in Florida, recent crown rot epidemics have been primarily caused by C. gloeosporioides. Little is known about the basic epidemiology of these important diseases on strawberry. The source of initial inoculum for epidemics in Israel, Florida (other US states including California) and the rest of the world is not well understood. Subspecies relationships between Colletotrichum isolates that cause the different diseases on strawberry (i.e. attack different tissues) are also not well understood. Objectives of this proposal were to detennine the potential of infested soil, strawberry debris and other hosts as sources of primary inoculum for strawberry diseases caused by Colletotrichum spp. in Israel and Florida. In addition, traditional (ie. morphological characteristics, benomyl sensitivity, vegetative compatibility grouping) and DNA based methods were used to investigate the etiology of these diseases in order to resolve epidemiologically important subspecies variation. In Israel it was found that C. gloeosporioides and C. acutatum infecting strawberry could remain viable in sterilized soil for up to one year and in methyl-bromide fumigated soil for up to 4 months; inoculum in mummified fruit remained viable for at least 5 months under field conditions whereas that in infected crowns was not recovered. Therefore, the contribution of these inocula to disease epidemics should be considered. The host range and specificity of C. acutatum from strawberry was examined on pepper, eggplant, tomato, bean and strawberry under greenhouse conditions. The fungus was recovered from all plant species over a three-month period but caused disease symptoms only on strawberry. C. acutatum was also isolated from healthy looking, asymptomatic plants of the weed species, Vicia and Conyza, growing in infected strawberry fruiting fields. Isolates of C. acutatum originating from strawberry and anemone infected both plant species in artificial inoculations. The habitation of a large number of plant species including weeds by C. acutatum suggests that although it causes disease only on strawberry and anemone in Israel, these plants may serve as a potential inoculum source for strawberry infection and pennit survival of the pathogen between seasons. In Florida, isolates of Colletotrichum spp. from diseased strawberry fruit and crowns were evaluated to detennine their etiology and the genetic diversity of the pathogens. Only C. acutatum was recovered from fruit and C. gloeosporioides were the main species recovered from crowns. These isolates were evaluated at 40 putative genetic loci using random amplified polymorphic DNA (RAPD). Genetic analysis of RAPD markers revealed that the level of linkage disequilibrium among polymorphic loci in C. gloeosporioides suggested that they were a sexually reproducing population. Under field conditions in Florida, it was detennined that C. gloeosporioides in buried crowns survived
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