ビーム理論とは何ですか？
Beam Theories ビーム理論 - The numerical results obtained are exposed and analyzed in detail to verify the validity of the current theory and prove the influence of the material composition, geometry, and shear deformation on the vibratory responses of FG beams, showing the impact of normal deformation on these responses which is neglected in most of the beam theories. [1] The focus of this work is on studying the deflection difference between both beam theories at different beam dimensions as well as showing the shape of rotation of the cross section while applying a nodal point load equation to simulate the moving load. [2] Beam theories such as the Timoshenko beam theory are in agreement with the elasticity theory. [3] The analytical models exploit both the framework of linear elastic fracture mechanics (LEFM) in a combination of analytical considerations and numerical results and one-dimensional (1D) beam theories, whereas the finite element predictions are conducted using the capabilities of the ABAQUS package and a standalone subroutine developed in MATLAB environment for post-processing the results of two-dimensional (2D) finite element analysis. [4] The aim is to derive a consistent asymptotic beam theory without the ad hoc assumptions usually made in the development of beam theories. [5] Furthermore, a comparison between the various micro-beam theories on the basis of modified couple stress theory, modified strain gradient theory, and classical theory are presented. [6] In order to enhance currently used beam theories in $$\mathbb {R}^2$$R2 and $$\mathbb {R}^3$$R3 to include mechanisms of dissipation and memory, it is necessary to establish if the mathematical models for these theories can be derived using the conservation and the balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. [7] By invoking the uniform-approximation method in combination with the pseudo-reduction technique, a hierarchy of beam theories of different orders of approximation is established. [8] Classical finite element (FE) beam theories are based on displacement formulation requiring derivatives to obtain the stress components which leads to a large number of FEs and depend on nodal averaging techniques for achieving sufficient accuracy. [9] The edge bending wave on a thin isotropic semi-infinite plate reinforced by a beam is considered within the framework of the classical plate and beam theories. [10] Dynamics of a functionally graded (FG) beam were studied using Timoshenko and Euler-Bernoulli (EB) beam theories. [11] Performance and effectiveness of two different meshes—tetrahedral and hexahedral (brick-type)—are checked through comparison with results presented by classical plate and beam theories. [12] Double and multiple-Beam System (BS) models are structural models that idealize a system of beams interconnected by elastic layers, where beam theories are assumed to govern the beams and elastic foundation models are assumed to represent the elastic layers. [13] The main purpose of the current study was to overcome some deficiencies of commonly used beam theories, such as shear-locking, the lacking relevance of isotropic materials for multi-layer composites, the incompatibility with other continuum elements, and the limited continuity in interpolation. [14] However, for 3D structures having two dominating planar geometric dimensions, a more appropriate approximation demands the move from the use of beam theories to advance structural models. [15] Through the beam theories, the deflections of the rolls are carefully analyzed. [16] The solutions are generated by introducing unknown axially periodic displacement functions in place of the axially invariant warping functions in Iesan's rational scheme, due to the periodic characteristics of the beam structure, while retaining the displacement fields integrated from rigid-body displacements, which represent basic kinematics in beam theories. [17]得られた数値結果を公開して詳細に分析し、現在の理論の妥当性を検証し、材料組成、形状、およびせん断変形がFGビームの振動応答に及ぼす影響を証明し、これらの応答に対する通常の変形の影響を示します。ほとんどのビーム理論では無視されています。 [1] この作業の焦点は、異なるビーム寸法での両方のビーム理論間のたわみの違いを研究することと、移動荷重をシミュレートするために節点荷重方程式を適用しながら断面の回転の形状を示すことです。 [2] ティモシェンコビーム理論などのビーム理論は、弾性理論と一致しています。 [3] 解析モデルは、線形弾性破壊力学（LEFM）のフレームワークを、解析の考慮事項と数値結果および1次元（1D）ビーム理論の組み合わせで活用しますが、有限要素予測は、ABAQUSパッケージと2次元（2D）有限要素解析の結果を後処理するためにMATLAB環境で開発されたスタンドアロンサブルーチン。 [4] 目的は、ビーム理論の開発で通常行われるアドホックな仮定なしに、一貫した漸近ビーム理論を導出することです。 [5] さらに、修正対応力理論、修正ひずみ勾配理論、および古典理論に基づくさまざまなマイクロビーム理論の比較を示します。 [6] $$\mathbb {R}^2$$R2 と $$\mathbb {R}^3$$R3 で現在使用されているビーム理論を強化して、散逸と記憶のメカニズムを含めるには、数学的これらの理論のモデルは、対応する運動学的仮定と組み合わせて、連続体力学の保存法則と平衡法則を使用して導き出すことができます。 [7] 一様近似法を疑似縮小法と組み合わせて呼び出すことにより、異なる近似次数のビーム理論の階層が確立されます。 [8] 古典的な有限要素 (FE) ビーム理論は、多数の FE につながる応力成分を得るために導関数を必要とする変位定式化に基づいており、十分な精度を達成するための節点平均化技術に依存しています。 [9] ビームによって強化された薄い等方性半無限プレート上のエッジ曲げ波は、古典的なプレート理論とビーム理論の枠組みの中で考慮されます。 [10] ティモシェンコとオイラー ベルヌーイ (EB) ビーム理論を使用して傾斜機能 (FG) ビームのダイナミクスを研究しました。 [11] 2 つの異なるメッシュ (四面体と六面体 (レンガ型)) のパフォーマンスと有効性は、古典的なプレート理論とビーム理論によって提示された結果との比較を通じてチェックされます。 [12] ダブルおよびマルチビーム システム (BS) モデルは、弾性層によって相互接続されたビームのシステムを理想化する構造モデルです。ビーム理論はビームを支配すると想定され、弾性基礎モデルは弾性層を表すと想定されます。 [13] 現在の研究の主な目的は、シェアロッキング、多層複合材料に対する等方性材料の関連性の欠如、他の連続体要素との非互換性、および補間の制限された連続性など、一般的に使用されるビーム理論のいくつかの欠陥を克服することでした。 [14] ただし、2 つの支配的な平面の幾何学的寸法を持つ 3D 構造の場合、より適切な近似を行うには、ビーム理論の使用から構造モデルを進めることへの移行が必要です。 [15] ビーム理論により、ロールのたわみが注意深く分析されます。 [16] 解は、基本的な運動学を表す剛体変位から統合された変位場を保持しながら、ビーム構造の周期的特性により、Iesan の有理スキームの軸方向不変ワーピング関数の代わりに未知の軸方向周期変位関数を導入することによって生成されます。ビーム理論で。 [17]
nonlocal strain gradient
In present paper, a novel two variable shear deformation beam theories are developed and applied to investigate the combined effects of nonlocal stress and strain gradient on the bending and buckling behaviors of nanobeams by using the nonlocal strain gradient theory. [1] The particular feature is used to derive the generalized eigenvalue equation for free vibration analysis of AFGM beams in conjunction with the Euler-Bernoulli, the Timoshenko and the nonlocal strain gradient beam theories. [2] Different size-dependent beam theories have been considered, such as the classical beam theory, nonlocal beam theory, strain gradient beam theory and nonlocal strain gradient beam theory, in order to reveal small-scale effects. [3]現在の論文では、新しい2つの可変せん断変形ビーム理論が開発され、非局所ひずみ勾配理論を使用して、ナノビームの曲げおよび座屈挙動に対する非局所応力とひずみ勾配の複合効果を調査するために適用されます。 [1] 特定の機能は、オイラー-ベルヌーイ理論、ティモシェンコ理論、および非局所ひずみ勾配梁理論と組み合わせて、AFGM 梁の自由振動解析の一般化された固有値方程式を導出するために使用されます。 [2] nan [3]
higher order shear 高次せん断
The structural stability of a column with rectangular and circular cross-section under axial compression is studied based on various higher-order shear deformation beam theories. [1] In this paper the dynamic stability behaviour of single delaminated composite beam is investigated using higher order shear deformable beam theories. [2] Differing from the Euler–Bernoulli/Timoshenko beam theories, a higher-order shear beam deformation model that does neither require a shear correction factor nor need a planar cross-section assumption after deformation. [3]軸圧縮下の長方形および円形断面の柱の構造安定性は、さまざまな高次せん断変形梁理論に基づいて研究されています。 [1] この論文では、単一の剥離した複合梁の動的安定性挙動を、高次のせん断変形可能な梁理論を使用して調査します。 [2] nan [3]
Timoshenko Beam Theories ティモシェンコビーム理論
The Euler-Bernoulli and Timoshenko beam theories are utilized for defining the longitudinal and lateral deformation of the sandwich beam. [1] The simply-supported micro-beam is modeled utilizing Euler-Bernoulli and Timoshenko beam theories. [2] The simplified governing equations for Euler–Bernoulli and Timoshenko beam theories are successfully rediscovered using the present AI-Timoshenko method, which shows that this method is capable of discovering simplified governing equations for applied mechanics problems. [3] The free vibration of rotating functionally graded nanobeams under different boundary conditions is studied based on nonlocal elasticity theory within the framework of Euler-Bernoulli and Timoshenko beam theories. [4] Differing from the Euler–Bernoulli/Timoshenko beam theories, a higher-order shear beam deformation model that does neither require a shear correction factor nor need a planar cross-section assumption after deformation. [5] Free thermal vibration analysis of nanobeams surrounded by an elastic matrix is examined via nonlocal elasticity and Timoshenko beam theories in this article. [6] Finally, the Euler beam and Timoshenko beam theories combined with the transformed section method were used to obtain the stiffness of the combined GFRP members, and then compare those stiffness with the experimental results. [7] The nonlocal elasticity theory together with the Euler-Bernoulli and Timoshenko beam theories is used to model the present system. [8] In this paper is analyzed the difference that occurs in the displacements using the Bernoulli and Timoshenko beam theories by varying the relationship between span and height of the cross section and changing the boundary conditions of the structural element. [9] The flexural wave equations are established based on the Euler–Bernoulli and Timoshenko beam theories. [10] The matrix is implemented in the Ftool software, and its results are compared against several matrices found in the literature, with or without higher-order terms in the strain tensor, as well as the EulerBernoulli or Timoshenko beam theories. [11]オイラー-ベルヌーイおよびティモシェンコ梁理論は、サンドイッチ梁の縦方向および横方向の変形を定義するために利用されます。 [1] 単純に支持されたマイクロビームは、オイラーベルヌーイおよびティモシェンコビーム理論を利用してモデル化されています。 [2] nan [3] nan [4] nan [5] nan [6] 最後に、変換断面法と組み合わせたオイラー ビーム理論とティモシェンコ ビーム理論を使用して、結合した GFRP 部材の剛性を取得し、それらの剛性を実験結果と比較しました。 [7] Euler-Bernoulli および Timoshenko ビーム理論と共に非局所弾性理論を使用して、現在のシステムをモデル化します。 [8] nan [9] nan [10] nan [11]
Bernoulli Beam Theories ベルヌーイビーム理論
Both Timoshenko and Euler-Bernoulli beam theories are applied and local 2D effects due to near tip deformations are introduced through suitable analytically derived crack tip root rotations and displacements. [1] With the aids of Erigen's nonlocal elasticity, Euler-Bernoulli beam theories and van der Waal forces equation, systems of nonlinear partial differential equations governing the dynamics responses of slightly curved multi-walled carbon nanotubes resting on Winkler and Pasternak foundations in a thermal-magnetic environment are developed. [2] This theory can be reduced to the first strain gradient and classical Euler–Bernoulli beam theories. [3] Numerical studies validate the present model against three-dimensional finite element models and the thick-face sandwich theory, and compare it with the conventional Timoshenko and couple stress Euler–Bernoulli beam theories. [4] The nonlinear dynamics of functionally graded (FG) microbeams have been studied based on the von Karman nonlinear theory, the modified couple stress and Euler–Bernoulli beam theories. [5] The cantilever beam is modeled by using both Timoshenko and Euler–Bernoulli beam theories. [6]TimoshenkoとEuler-Bernoulliの両方のビーム理論が適用され、適切な解析的に導出された亀裂先端の根の回転と変位によって、先端付近の変形による局所的な2D効果が導入されます。 [1] Erigenの非局所弾性、オイラー-ベルヌーイビーム理論、ファンデルワール力方程式の助けを借りて、熱磁気環境でウィンクラーとパステルナックの基礎上にあるわずかに湾曲した多層カーボンナノチューブのダイナミクス応答を支配する非線形偏微分方程式のシステム開発されています。 [2] nan [3] 数値研究は、現在のモデルを 3 次元有限要素モデルおよび厚面サンドイッチ理論に対して検証し、それを従来のティモシェンコおよび結合応力オイラー-ベルヌーイ ビーム理論と比較します。 [4] 傾斜機能 (FG) マイクロビームの非線形ダイナミクスは、フォン カルマン非線形理論、修正対応力、オイラー ベルヌーイ ビーム理論に基づいて研究されています。 [5] nan [6]
Different Beam Theories 異なるビーム理論
Applications of different beam theories for both axial and bending vibrations have enabled the examination of the role played by rigid-body parameters on the multi-body system's dynamic behaviour. [1] This chapter investigates the influence of the different beam theories, i. [2] In this paper, bending and buckling behavior of nanobeam utilizing different beam theories including Timoshenko, Euler–Bernoulli, and higher-order beam theories are developed to investigate. [3] The governing equations of motion are derived in framework of a unified beam theory (which includes different beam theories such as Euler–Bernoulli, Timoshenko and Reddy beam theories as special case), and Hamilton’s principle. [4] The deduction of load–deflection relationship is established using different beam theories. [5] The governing equations of motion are derived in framework of a unified beam theory (which includes different beam theories such as Euler–Bernoulli, Timoshenko and Reddy beam theories as special case), and Hamilton’s principle. [6]軸方向振動と曲げ振動の両方に異なるビーム理論を適用することで、マルチボディシステムの動的挙動における剛体パラメータが果たす役割を調べることができました。 [1] この章では、さまざまなビーム理論の影響を調査します。 [2] この論文では、Timoshenko、Euler-Bernoulli、および高次ビーム理論を含むさまざまなビーム理論を利用したナノビームの曲げおよび座屈挙動を調査するために開発しました。 [3] 運動の支配方程式は、統一されたビーム理論 (特殊なケースとして Euler-Bernoulli、Timoshenko、Reddy ビーム理論などの異なるビーム理論を含む) とハミルトンの原理の枠組みで導出されます。 [4] nan [5] nan [6]
Order Beam Theories
In higher-order beam theories, cross-sectional deformations causing complex responses of thin-walled beams are considered as additional degrees of freedom. [1] Several common as well as higher-order beam theories are chosen as test examples to derive and compare the key wave parameters to evaluate the effects of shear deformation and rotary inertia for wave propagation in near-field and far-field regions. [2] An up-to-date problem in analysis of composite beams is to analyze higher-order beam theories with a considerable number of displacement variables and evaluate the influence of each term in order to reduce the model computational cost. [3] Compared to the traditional beam elements and other beam formulations based on higher-order beam theories, we improved the kinematic description of member cross-section displacement field, where the kinematic parameterization is performed on two scales, i. [4] In addition, as compared with nonlocal Euler–Bernoulli beam, the shear effect is evident, and an additional scale effect is captured, indicating the importance of applying higher-order beam theories in the analysis of nanostructures. [5] The variationally consistent methodology for generating state space models of 1D composite beams is evolved systematically and used to establish such models corresponding to different composite higher order beam theories. [6]高次のビーム理論では、薄肉ビームの複雑な応答を引き起こす断面変形は、追加の自由度と見なされます。 [1] いくつかの一般的なビーム理論と高次ビーム理論がテスト例として選択され、主要な波動パラメーターを導出および比較して、ニアフィールドおよびファーフィールド領域での波動伝搬に対するせん断変形と回転慣性の影響を評価します。 [2] 複合梁の解析における最新の問題は、モデルの計算コストを削減するために、かなりの数の変位変数を使用して高次の梁理論を解析し、各項の影響を評価することです。 [3] nan [4] nan [5] nan [6]
Classical Beam Theories 古典的なビーム理論
For the validation of the proposed model, various buckling, post-buckling and nonlinear bending tests are carried out and the obtained results are compared with the results of classical beam theories and 2D/3D finite element results. [1] To highlight this fact, this paper compares classical beam theories with refined ones based on the Carrera Unified Formulation (CUF) and the shell results using the commercial finite element (FE) software and the data available from the literature. [2] Besides, unlike the former studies which rely on classical beam theories, the first-order shear deformation beam theory is used to obtain more accurate estimations of shape memory alloy-wire hysteresis loops and their decaying characteristics. [3] First, Reddy (third order) and classical beam theories are used in the formulation. [4]提案されたモデルの検証のために、さまざまな座屈、座屈後、および非線形曲げ試験が実行され、得られた結果が従来の梁理論の結果および2D/3D有限要素結果と比較されます。 [1] この事実を強調するために、この論文では、古典的なビーム理論を、カレラ統一定式化（CUF）に基づく洗練されたものと比較し、市販の有限要素（FE）ソフトウェアと文献から入手可能なデータを使用したシェルの結果を比較します。 [2] さらに、古典的なビーム理論に依存する以前の研究とは異なり、一次せん断変形ビーム理論を使用して、形状記憶合金ワイヤ ヒステリシス ループとその減衰特性のより正確な推定値を取得します。 [3] まず、Reddy (3 次) と古典的なビーム理論が定式化に使用されます。 [4]
Refined Beam Theories
First, classical and refined beam theories are combined at the element level via a nodedependent kinematic (NDK) concept, which was recently introduced by the authors. [1] In former, the refined beam theories are obtained on the basis of Taylor and Lagrange-type expansions. [2] In this article, 1 D refined beam theories based on Carrera Unified Formulation (CUF) and the Isogeometric approach (IGA) are synthesized for the free vibration analysis of laminated beam structure. [3]まず、古典的なビーム理論と洗練されたビーム理論が、ノード依存運動学（NDK）の概念を介して要素レベルで組み合わされます。 著者によって紹介されました。 [1] 前者では、洗練されたビーム理論は、テイラーおよびラグランジュ型の展開に基づいて得られます。 [2] この記事では、積層ビーム構造の自由振動解析のために、Carrera Unified Formulation (CUF) と Isogeometric アプローチ (IGA) に基づく 1 D 改良ビーム理論を合成します。 [3]
Deformation Beam Theories
The structural stability of a column with rectangular and circular cross-section under axial compression is studied based on various higher-order shear deformation beam theories. [1] In present paper, a novel two variable shear deformation beam theories are developed and applied to investigate the combined effects of nonlocal stress and strain gradient on the bending and buckling behaviors of nanobeams by using the nonlocal strain gradient theory. [2]軸圧縮下の長方形および円形断面の柱の構造安定性は、さまざまな高次せん断変形梁理論に基づいて研究されています。 [1] 現在の論文では、新しい2つの可変せん断変形ビーム理論が開発され、非局所ひずみ勾配理論を使用して、ナノビームの曲げおよび座屈挙動に対する非局所応力とひずみ勾配の複合効果を調査するために適用されます。 [2]
Known Beam Theories
Analytical relationships for elastic modulus, yield stress, and Poisson’s ratio of the 3D re-entrant unit cell are derived based on two well-known beam theories namely Euler–Bernoulli and Timoshenko. [1] An analytical model based on the known beam theories was used to assess the accuracy of the measurements. [2]Deformable Beam Theories 変形可能なビーム理論
In this paper the dynamic stability behaviour of single delaminated composite beam is investigated using higher order shear deformable beam theories. [1] In this paper, the nonlinear dynamic response of two-directional functionally graded (2D-FG) microbeam incorporating geometrically imperfect effect is investigated via a unified shear deformable beam theory, which can degenerate into several previous theories including Euler-Bernoulli, Timoshenko, and Reddy shear deformable beam theories. [2]この論文では、単一の剥離した複合梁の動的安定性挙動を、高次のせん断変形可能な梁理論を使用して調査します。 [1] この論文では、幾何学的に不完全な効果を組み込んだ2方向機能傾斜（2D-FG）マイクロビームの非線形動的応答を、オイラー-ベルヌーイ、ティモシェンコ、レディを含むいくつかの以前の理論に縮退できる統一せん断変形可能ビーム理論を介して調査します。せん断変形可能なビーム理論。 [2]