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A Non-Local Third Order Theory of Functionally Graded Plates Under Electromechanical Coupling Effect

機譯：機電耦合作用下功能梯度板的非局部三階理論

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摘要

In this research, a general nonlinear third-order plate theory has been developed using the principle of virtual displacements. The developed theory is based on geometric nonlinearity, size effects of structures in micro scale, functionally graded materials, and piezoelectric effects. The von Karman nonlinear strains, i.e., small strain and moderate rotation, are considered to represent geometric nonlinearity. A modified couple stress theory is adopted to capture microstructure dependent size effect. A power law distribution is used to represent the variation of two material constituents through thickness. The developed plate theory is also specialized to classical, first order shear deformation, and Reddy third order plate theories.;Analytical solutions for the developed plate theory are presented using the Navier solution technique. All dependent variables are assumed to be forms of double trigonometric functions which satisfy the boundary conditions. The analytical solutions are limited to geometric linearity and simply supported plates. Examples of bending, buckling, and vibration problems are presented to show effects of the power-law distribution of two materials and the microstructure-dependent size parameter.;The nonlinear finite element model based on the developed plate theory is carried out to study of the static bending problems regarding the size effects of microstructure, geometric nonlinearity, and power-law variation of the material composition through the thickness. The principle of virtual work is utilized to develop a displacement based weak-form Galerkin finite element model which requires C1 continuity of all dependent variables. A conforming element is implemented using Hermite type interpolation functions.;The piezoelectric effect is considered for functionally graded smart plates which have surface-mounted piezoelectric layers, and a functionally graded core layer. The formulation includes the coupling between mechanical deformations and the charge equations of electrostatics. In addition to the kinematic assumption of the developed plate theory, the potential function is assumed to be the combination of half cosine variation of electric potential and linear variation of applied voltage on outer surfaces. An analytical solution and a finite element model are obtained. A parametric study is presented to show effects of thickness ratio between core layer and piezoelectric layers in addition to material variation of core plate and micro structure size effects.
機譯：在這項研究中，利用虛擬位移原理開發(fā)了通用的非線性三階板理論。發(fā)達的理論基于幾何非線性，微觀尺度結(jié)構(gòu)的尺寸效應(yīng)，功能梯度材料和壓電效應(yīng)。 von Karman非線性應(yīng)變，即小應(yīng)變和適度旋轉(zhuǎn)，被認(rèn)為代表了幾何非線性。采用改進的耦合應(yīng)力理論來捕獲微結(jié)構(gòu)相關(guān)的尺寸效應(yīng)。冪律分布用于表示兩種材料成分隨厚度的變化。發(fā)達的板理論還專門用于經(jīng)典的一階剪切變形和Reddy的三階板理論。假定所有因變量均為滿足邊界條件的雙三角函數(shù)形式。分析解決方案僅限于幾何線性和簡單支撐的板。給出了彎曲，屈曲和振動問題的實例，以顯示兩種材料的冪律分布和與微觀結(jié)構(gòu)有關(guān)的尺寸參數(shù)的影響。；基于發(fā)達的板理論，建立了非線性有限元模型，以研究材料的屈曲，屈曲和振動問題。靜態(tài)彎曲問題，涉及微觀結(jié)構(gòu)的尺寸效應(yīng)，幾何非線性和厚度方向上材料成分的冪律變化。虛擬工作原理用于開發(fā)基于位移的弱形式Galerkin有限元模型，該模型需要所有因變量的C1連續(xù)性。使用Hermite型插值函數(shù)可實現(xiàn)一致性元素。;對于具有表面貼裝壓電層和功能漸變核心層的功能漸變智能板，應(yīng)考慮壓電效應(yīng)。該公式包括機械變形與靜電電荷方程之間的耦合。除了已發(fā)展的板理論的運動學(xué)假設(shè)外，還假設(shè)電勢函數(shù)是電勢的半余弦變化與外表面施加電壓的線性變化的組合。得到了解析解和有限元模型。提出了一項參數(shù)研究，以顯示核心層和壓電層之間的厚度比的影響，以及核心板的材料變化和微觀結(jié)構(gòu)尺寸的影響。

著錄項

  • 作者

    Kim, Jinseok.;

  • 作者單位

    Texas A&M University.;

  • 授予單位 Texas A&M University.;
  • 學(xué)科 Mechanical engineering.
  • 學(xué)位 Ph.D.
  • 年度 2017
  • 頁碼 184 p.
  • 總頁數(shù) 184
  • 原文格式 PDF
  • 正文語種 eng
  • 中圖分類
  • 關(guān)鍵詞

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