• Title/Summary/Keyword: fully nonlinear term

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AN APPLICATION OF LINKING THEOREM TO FOURTH ORDER ELLIPTIC BOUNDARY VALUE PROBLEM WITH FULLY NONLINEAR TERM

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.22 no.2
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    • pp.355-365
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    • 2014
  • We show the existence of nontrivial solutions for some fourth order elliptic boundary value problem with fully nonlinear term. We obtain this result by approaching the variational method and using a linking theorem. We also get a uniqueness result.

Nonlinear modelling and analysis of thin piezoelectric plates: Buckling and post-buckling behaviour

  • Krommer, Michael;Vetyukova, Yury;Staudigl, Elisabeth
    • Smart Structures and Systems
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    • v.18 no.1
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    • pp.155-181
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    • 2016
  • In the present paper we discuss the stability and the post-buckling behaviour of thin piezoelastic plates. The first part of the paper is concerned with the modelling of such plates. We discuss the constitutive modelling, starting with the three-dimensional constitutive relations within Voigt's linearized theory of piezoelasticity. Assuming a plane state of stress and a linear distribution of the strains with respect to the thickness of the thin plate, two-dimensional constitutive relations are obtained. The specific form of the linear thickness distribution of the strain is first derived within a fully geometrically nonlinear formulation, for which a Finite Element implementation is introduced. Then, a simplified theory based on the von Karman and Tsien kinematic assumption and the Berger approximation is introduced for simply supported plates with polygonal planform. The governing equations of this theory are solved using a Galerkin procedure and cast into a non-dimensional formulation. In the second part of the paper we discuss the stability and the post-buckling behaviour for single term and multi term solutions of the non-dimensional equations. Finally, numerical results are presented using the Finite Element implementation for the fully geometrically nonlinear theory. The results from the simplified von Karman and Tsien theory are then verified by a comparison with the numerical solutions.

Experimental Study for the Long-term Behavior of Shear Wall (전단벽의 장기거동 특성에 관한 실험적 연구)

  • 권승희;김진근
    • Proceedings of the Korea Concrete Institute Conference
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    • 2001.11a
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    • pp.197-202
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    • 2001
  • It is necessary to Investigate long-term behavior of vertical members such as column and shear wall because the long-term behavior induces the serviceability problem of reinforce-concrete structures. However, the long-term behavior on shear wall has not been fully studied. Experimental works are performed to understand the time dependent behavior of shear wall, especially the effect of loading area in this research. Three different types of cross sections are adopted, i.e., 10$\times$10 cm, 10$\times$30 cm, and 10$\times$50 cm with the same loading area of 10$\times$10 cm. The creep strains were different from point to point in the section of the shear wall specimen because of the nonlinear stress distribution. The effect of the nonlinear stress distribution was larger in the specimen with the larger width.

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Soil-pile interaction effects in wharf structures under lateral loads

  • Doran, Bilge;Seckin, Aytug
    • Structural Engineering and Mechanics
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    • v.51 no.2
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    • pp.267-276
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    • 2014
  • Wharfs are essential to shipping and support very large gravity loads on both a short-term and long-term basis which cause quite large seismic internal forces. Therefore, these structures are vulnerable to seismic activities. As they are supported on vertical and/or batter piles, soil-pile interaction effects under earthquake events have a great importance in seismic resistance which is not yet fully understood. Seismic design codes have become more stringent and suggest the use of new design methods, such as Performance Based Design principles. According to Turkish Code for Coastal and Port Structures (TCCS 2008), the interaction between soil and pile should somehow be considered in the nonlinear analysis in an accurate manner. This study aims to explore the lateral load carrying capacity of recently designed wharf structures considering soil-pile interaction effects for different soil conditions. For this purpose, nonlinear structure analysis according to TCCS (2008) has been performed comparing simplified and detailed modeling results.

Quantification of nonlinear seismic response of rectangular liquid tank

  • Nayak, Santosh Kumar;Biswal, Kishore Chandra
    • Structural Engineering and Mechanics
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    • v.47 no.5
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    • pp.599-622
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    • 2013
  • Seismic response of two dimensional liquid tanks is numerically simulated using fully nonlinear velocity potential theory. Galerkin-weighted-residual based finite element method is used for solving the governing Laplace equation with fully nonlinear free surface boundary conditions and also for velocity recovery. Based on mixed Eulerian-Lagrangian (MEL) method, fourth order explicit Runge-Kutta scheme is used for time integration of free surface boundary conditions. A cubic-spline fitted regridding technique is used at every time step to eliminate possible numerical instabilities on account of Lagrangian node induced mesh distortion. An artificial surface damping term is used which mimics the viscosity induced damping and brings in numerical stability. Four earthquake motions have been suitably selected to study the effect of frequency content on the dynamic response of tank-liquid system. The nonlinear seismic response vis-a-vis linear response of rectangular liquid tank has been studied. The impulsive and convective components of hydrodynamic forces, e.g., base shear, overturning base moment and pressure distribution on tank-wall are quantified. It is observed that the convective response of tank-liquid system is very much sensitive to the frequency content of the ground motion. Such sensitivity is more pronounced in shallow tanks.

HIGHER ORDER DISCONTINUOUS GALERKIN FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

  • Ohm, Mi Ray;Lee, Hyun Young;Shin, Jun Yong
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.18 no.4
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    • pp.337-350
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    • 2014
  • In this paper, we consider discontinuous Galerkin finite element methods with interior penalty term to approximate the solution of nonlinear parabolic problems with mixed boundary conditions. We construct the finite element spaces of the piecewise polynomials on which we define fully discrete discontinuous Galerkin approximations using the Crank-Nicolson method. To analyze the error estimates, we construct an appropriate projection which allows us to obtain the optimal order of a priori ${\ell}^{\infty}(L^2)$ error estimates of discontinuous Galerkin approximations in both spatial and temporal directions.

HIGHER ORDER OF FULLY DISCREATE SOLUTION FOR PARABOLIC PROBLEM IN $L_{\infty}$

  • Lee, H.Y.;Lee, J.R.
    • Journal of applied mathematics & informatics
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    • v.4 no.1
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    • pp.17-30
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    • 1997
  • In this work we approximate the solution of initialboun-dary value problem using a Galerkin-finite element method for the spatial discretization and Implicit Runge-Kutta method for the spatial discretization and implicit Runge-Kutta methods for the time stepping. To deal with the nonlinear term f(x, t, u), we introduce the well-known extrapolation sheme which was used widely to prove the convergence in $L_2$-norm. We present computational results showing that the optimal order of convergence arising under $L_2$-norm will be preserved in $L_{\infty}$-norm.

UNCONDITIONALLY STABLE GAUGE-UZAWA FINITE ELEMENT METHODS FOR THE DARCY-BRINKMAN EQUATIONS DRIVEN BY TEMPERATURE AND SALT CONCENTRATION

  • Yangwei Liao;Demin Liu
    • Bulletin of the Korean Mathematical Society
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    • v.61 no.1
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    • pp.93-115
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    • 2024
  • In this paper, the Gauge-Uzawa methods for the Darcy-Brinkman equations driven by temperature and salt concentration (DBTC) are proposed. The first order backward difference formula is adopted to approximate the time derivative term, and the linear term is treated implicitly, the nonlinear terms are treated semi-implicit. In each time step, the coupling elliptic problems of velocity, temperature and salt concentration are solved, and then the pressure is solved. The unconditional stability and error estimations of the first order semi-discrete scheme are derived, at the same time, the unconditional stability of the first order fully discrete scheme is obtained. Some numerical experiments verify the theoretical prediction and show the effectiveness of the proposed methods.