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In this paper, a nonlinear analysis of three-dimensional steel frames is developed. This analysis accounts for material and geometric nonlinearities. The material nonlinearity considers the gradual yielding associated with member ...
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In this paper, a nonlinear analysis of three-dimensional steel frames is developed. This analysis accounts for material and geometric nonlinearities. The material nonlinearity considers the gradual yielding associated with member forces. The geometric nonlinearioty includes the second-order effects associated with P-δ and P-△. The material nonlinearity at a section is considered using the concept of the P-m hinge consisting of many fibers. The geometric nonlinearity is considered by the use of stability functions. The modified incremental displace- ment method is used as the solution technique. The load-displacement relationships predicted by the proposed analysis compare well with those given by other approaches.
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In this paper, the stability of supersonic contact discontinuities in the threedimensional compressible isentropic steady Euler flows is investigated by using the nonlinear geometric optics. We construct the asymptotic expansions ...
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In this paper, the stability of supersonic contact discontinuities in the threedimensional compressible isentropic steady Euler flows is investigated by using the nonlinear geometric optics. We construct the asymptotic expansions of highly oscillatory contact discontinuities when a planar contact discontinuity is perturbed by a small amplitude high frequency oscillatory incident wave, and deduce there exists a large amplification of amplitudes in the reflected and refracted oscillatory waves when the high frequency oscillatory wave strikes the contact discontinuity front at three critical angles. Moreover, we obtain that the leading profiles of highly oscillatory waves are described by an initial boundary value problem of Burgerstransport equations, and the leading profile of contact discontinuity front satisfies an initial value problem of a Hamilton-Jacobi equation, respectively. The amplification phenomenon shows that this supersonic contact discontinuity is only weakly stable in the sense of Wang and Yu [“Stability of contact discontinuities in three-dimensional compressible steady flows,” J. Differ. Equ. 255, 1278-1356 (2013)]
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In this paper a general nonlinear third-order plate theory that accounts for (a) geometric nonlinearity, (b) microstructure-dependent size effects, and (c) two-constituent material variation through the plate thickness (i.e., func...
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In this paper a general nonlinear third-order plate theory that accounts for (a) geometric nonlinearity, (b) microstructure-dependent size effects, and (c) two-constituent material variation through the plate thickness (i.e., functionally graded material plates) is presented using the principle of virtual displacements. A detailed derivation of the equations of motion, using Hamilton's principle, is presented, and it is based on a modified couple stress theory, power-law variation of the material through the thickness, and the von Karman nonlinear strains. The modified couple stress theory includes a material length scale parameter that can capture the size effect in a functionally graded material. The governing equations of motion derived herein for a general third-order theory with geometric nonlinearity, microstructure dependent size effect, and material gradation through the thickness are specialized to classical and shear deformation plate theories available in the literature. The theory presented herein also can be used to develop finite element models and determine the effect of the geometric nonlinearity, microstructure-dependent size effects, and material grading through the thickness on bending and postbuckling response of elastic plates. Third-order shear deformation plate theory; Functionally graded materials; Modified couple stress
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The electromagnetic force a photon undergoes in a nonlinear regime can be geometrized. This is a rather unexpected result and at the same time a beautiful consequence of the analysis of the behavior of the discontinuities of non-h...
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The electromagnetic force a photon undergoes in a nonlinear regime can be geometrized. This is a rather unexpected result and at the same time a beautiful consequence of the analysis of the behavior of the discontinuities of non-homogeneous nonlinear electromagnetic field. We show how such geometrization is possible. [References: 5]
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In this paper, topology optimization of both geometrically and materially nonlinear structure is studied using a general displacement functional as the objective function. In order to consider large deformation, effective stress a...
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In this paper, topology optimization of both geometrically and materially nonlinear structure is studied using a general displacement functional as the objective function. In order to consider large deformation, effective stress and strain are expressed in terms of 2nd Piolar—Kirchhoff stress tensor and Green-Lagrange strain tensor, and constitutive equation is derived from the relation between the effective stress and strain. Sensitivity analysis of the general displacement functional is derived using the adjoint method. Numerical results of mean compliance design are compared under linear analysis, geometrical nonlinear analysis, material nonlinear analysis, and combined nonlinear analysis.
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External prestressing is achieving widespread success. However, some practical rules are not yet well established. An important question deals with the maximum distance between anchorages and deviators. Due to the absence of conta...
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External prestressing is achieving widespread success. However, some practical rules are not yet well established. An important question deals with the maximum distance between anchorages and deviators. Due to the absence of contact between the tendons and the concrete beam (other than at the anchorages and deviators), the change in the deformed shape of the concrete beam involves changes in the position of the tendons with respect to the center of gravity of the concrete beam (second-order effects), so that their influence on the equilibrium conditions of the beam near collapse can be significant. This paper suggests a simple equation that determines the maximum clear length of the tendons small enough not to take into account the second-order effects in common practice. A parametric analysis (made by means of a numerical method previously verified by comparisons with experimental test results) verifies the reliability of the simple equation suggested.
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The logarithmic strain measure is used to obtain a consistent geometric nonlinear finite element formulation to deal with large strains on space trusses. The formulation is based on the positional formulation and no local system o...
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The logarithmic strain measure is used to obtain a consistent geometric nonlinear finite element formulation to deal with large strains on space trusses. The formulation is based on the positional formulation and no local system of coordinates on the elements is needed to describe its kinematics. Three numerical examples are presented, including a tensegrity tower and a double layer elastoplastic space truss. The paper proves that the positional nonlinear formulation is valid for other objective strain measures used in the classical nonlinear formulations, i.e. logarithmic strain measure.
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The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct...
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The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). This work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing. Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.
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This paper presents a case study in which the finite element model for a curved circular plate -is calibrated to reproduce both the linear and nonlinear dynamic response measured from two nominally identical samples. The linear dy...
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This paper presents a case study in which the finite element model for a curved circular plate -is calibrated to reproduce both the linear and nonlinear dynamic response measured from two nominally identical samples. The linear dynamic response is described with the linear natural frequencies and mode shapes identified with a roving hammer test. Due to the uncertainty in the stiffness characteristics from the manufactured perforations, the linear natural frequencies are used to update the effective modulus of elasticity of the full order finite element model (FEM). The nonlinear dynamic response is described with nonlinear normal modes (NNMs) measured using force appropriation and high speed 3D digital image correlation (3D-DIC). The measured NNMs are used to update the boundary conditions of the full order FEM through comparison with NNMs calculated from a nonlinear reduced order model (NLROM). This comparison revealed that the nonlinear behavior could not be captured without accounting for the small curvature of the plate from manufacturing as confirmed in literature. So, 3D-DIC was also used to identify the initial static curvature of each plate and the resulting curvature was included in the full order FEM. The updated models are then used to understand how the stress distribution changes at large response amplitudes providing a possible explanation of failures observed during testing. (C) 2016 Elsevier Ltd. All rights reserved.
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This work deals with nonlinear geometric plates in the context of von Karman's theory. The formulation is written such that only the boundary in-plane displacement and deflection integral equations for boundary collocations are re...
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This work deals with nonlinear geometric plates in the context of von Karman's theory. The formulation is written such that only the boundary in-plane displacement and deflection integral equations for boundary collocations are required. At internal points, only out-of-plane rotation, curvature and in-plane internal force representations are used. Thus, only integral representations of these values are derived. The nonlinear system of equations is derived by approximating all densities in the domain integrals as single values, which therefore reduces the computational effort needed to evaluate the domain value influences. Hyper-singular equations are avoided by approximating the domain values using only internal nodes. The solution is obtained using a Newton scheme for which a consistent tangent operator was derived.
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