## 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. 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。

A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams

## 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. 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。

Effect of warping shape on buckling of circular and rectangular columns under axial compression

## In this paper the dynamic stability behaviour of single delaminated composite beam is investigated using higher order shear deformable beam theories. 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。

Dynamic stability analysis of delaminated composite beams in frequency domain using a unified beam theory with higher order displacement continuity

## The Euler-Bernoulli and Timoshenko beam theories are utilized for defining the longitudinal and lateral deformation of the sandwich beam. 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。

Effect of axially graded constraining layer on the free vibration properties of three layered sandwich beams with magnetorheological fluid core

## The simply-supported micro-beam is modeled utilizing Euler-Bernoulli and Timoshenko beam theories. 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。

Free Vibration Analysis of Rotating Beams Based on the Modified Couple Stress Theory and Coupled Displacement Field

## 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. 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。

An analytical solution for the inverted four-point bending test in orthotropic specimens

## 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. 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。

Coupled effects of magnetic field, number of walls, geometric imperfection, temperature change, and boundary conditions on nonlocal nonlinear vibration of carbon nanotubes resting on elastic foundations

## 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. 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。

An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies

## This chapter investigates the influence of the different beam theories, i. この章では、さまざまなビーム理論の影響を調査します。

Comparison of the Approaches

## In higher-order beam theories, cross-sectional deformations causing complex responses of thin-walled beams are considered as additional degrees of freedom. 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。

Higher-order beam bending theory for static, free vibration, and buckling analysis of thin-walled rectangular hollow section beams

## 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. 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。

A method for selection of structural theories for low to high frequency vibration analyses

## 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. 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。

Buckling, post-buckling and geometrically nonlinear analysis of thin-walled beams using a hypothetical layered composite cross-sectional model

## 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. 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。

Benchmarks for higher-order modes evaluation in the free vibration response of open thin-walled beams due to the cross-sectional deformations

## 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. 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。

Node-Dependent Kinematics and Multidimensional Finite Elements for the Analysis of Single/Double Swept, Composite Helicopter Blades

## In former, the refined beam theories are obtained on the basis of Taylor and Lagrange-type expansions. 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。

Comparison of classical and refined beam models applied on isotropic and FG thin-walled beams in nonlinear buckling response

## 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. 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。

Effect of warping shape on buckling of circular and rectangular columns under axial compression

## 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. 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。

A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams

## 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.

Idealized 3D Auxetic Mechanical Metamaterial: An Analytical, Numerical, and Experimental Study

## An analytical model based on the known beam theories was used to assess the accuracy of the measurements.

Simultaneous position and displacement sensing using two fibre Bragg grating sensors

## In this paper the dynamic stability behaviour of single delaminated composite beam is investigated using higher order shear deformable beam theories. 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。

Dynamic stability analysis of delaminated composite beams in frequency domain using a unified beam theory with higher order displacement continuity

## 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. 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。

Nonlinear dynamics of two-directional functionally graded microbeam with geometrical imperfection using unified shear deformable beam theory

## 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. 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。

A Refined Theory for Bending Vibratory Analysis of Thick Functionally Graded Beams

## 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. 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。

Analysis of Tapered Timoshenko and Euler–Bernoulli Beams on an Elastic Foundation with Moving Loads

## Beam theories such as the Timoshenko beam theory are in agreement with the elasticity theory. 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。

Free vibration analysis of nonlocal nanobeams: a comparison of the one-dimensional nonlocal integral Timoshenko beam theory with the two-dimensional nonlocal integral elasticity theory

## 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. 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。

Debonding Resistance Evaluation in Virtual Testing of Sandwich Specimens

## The aim is to derive a consistent asymptotic beam theory without the ad hoc assumptions usually made in the development of beam theories. 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。

Asymptotic beam theory for non-classical elastic materials

## 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. 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。

Structural instability of non-conservative functionally graded micro-beams tunable with piezoelectric layers

## 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. \$\$\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。

Thermodynamic consistency of beam theories in the context of classical and non-classical continuum mechanics and a thermodynamically consistent new formulation

## 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. 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。

A Beam—Just a Beam in Linear Plane Bending

10.1016/J.COMPOSITESB.2019.03.063

## 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. 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。

Generalized multifield variational formulation with interlaminar stress continuity for multilayered anisotropic beams

## 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. 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。

The edge bending wave on a plate reinforced by a beam (L).

10.1016/J.COMPSTRUCT.2018.09.021

## Dynamics of a functionally graded (FG) beam were studied using Timoshenko and Euler-Bernoulli (EB) beam theories. 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。

Dynamics of a functionally graded Timoshenko beam considering new spectrums

## 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. 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。

On the convergence of solid meshes for the prediction of part distortions due to residual stresses

## 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. 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。

Bending analysis of elastically connected Euler–Bernoulli double-beam system using the direct boundary element method

10.1016/J.COMPOSITESB.2018.10.073

## 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. 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。

NURBS-based modeling of laminated composite beams with isogeometric displacement-only theory

## 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. 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。

Bending and Vibration of Microstructure-Dependent Kirchhoff Microplates and Finite Element Implementations with R

## Through the beam theories, the deflections of the rolls are carefully analyzed. 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。

Analysis of deformations of rolls in the six-high tandem mill on the basis of anti-symmetry rotation

## 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. 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。

On the solutions to the Saint–Venant problem of heterogeneous beam-like structures with periodic microstructures