A Beam Theory for Anisotropic Materials

1985 ◽  
Vol 52 (2) ◽  
pp. 416-422 ◽  
Author(s):  
O. A. Bauchau
Keyword(s):  
Basic Assumption ◽  
Variational Principles ◽  
Axial Stress ◽  
Beam Theory ◽  
Short Review ◽  
Cross Sectional ◽  
Out Of Plane ◽  
In Series ◽  
Axial Stress Distribution ◽  
Energy Principles

Beam theory plays an important role in structural analysis. The basic assumption is that initially plane sections remain plane after deformation, neglecting out-of-plane warpings. Predictions based on these assumptions are accurate for slender, solid, cross-sectional beams made out of isotropic materials. The beam theory derived in this paper from variational principles is based on the sole kinematic assumption that each section is infinitely rigid in its own plane, but free to warp out of plane. After a short review of the Bernoulli and Saint-Venant approaches to beam theory, a set of orthonormal eigenwarpings is derived. Improved solutions can be obtained by expanding the axial displacements or axial stress distribution in series of eigenwarpings and using energy principles to derive the governing equations. The improved Saint-Venant approach leads to fast converging solutions and accurate results are obtained considering only a few eigenwarping terms.

A Beam Theory for Large Global Rotation, Moderate Local Rotation, and Small Strain

1988 ◽  
Vol 55 (1) ◽  
pp. 179-184 ◽  
Author(s):  
D. A. Danielson ◽  
D. H. Hodges
Keyword(s):  
Cross Section ◽  
Variational Principles ◽  
Beam Theory ◽  
Small Strain ◽  
General Context ◽  
Equilibrium Equations ◽  
Cross Sectional ◽  
Local Rotation ◽  
Material Points

Kinematical relations are derived to account for the finite cross-sectional warping occurring in a beam undergoing large deflections and rotations due to deformation. The total rotation at any point in the beam is represented as a large global rotation of the reference triad (a frame which moves nominally with the reference cross section material points), a small rotation that is constant over the cross section and is due to shear, and a local rotation whose magnitude may be small to moderate and which varies over a given cross section. Appropriate variational principles, equilibrium equations, boundary conditions, and constitutive laws are obtained. Two versions are offered: an intrinsic theory without reference to displacements, and an explicit theory with global rotation characterized by a Rodrigues vector. Most of the formulas herein have been published, but we reproduce them here in a new concise notation and a more general context. As an example, the theory is shown to predict behavior that agrees with published theoretical and experimental results for extension and torsion of a pretwisted strip. The example also helps to clarify the role of local rotation in the kinematics.

scholarly journals Experimental Investigation of Steel Plate Shear Walls under Shear-Compression Interaction

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Yang Lv ◽  
Ling Li ◽  
Di Wu ◽  
Bo Zhong ◽  
Yu Chen ◽  
...  
Keyword(s):  
Stress Distribution ◽  
Steel Plate ◽  
Axial Stress ◽  
Shear Walls ◽  
Shear Capacity ◽  
Steel Plate Shear Walls ◽  
Steel Plate Shear Wall ◽  
Gravity Load ◽  
Moment Resisting ◽  
Axial Stress Distribution

Four scaled one-storey single-bay steel plate shear wall (SPSW) specimens with unstiffened panels were tested to determine their behaviour under cyclic loadings. The shear walls had moment-resisting beam-to-column connections. Four different vertical loads, i.e., 300 kN, 600 kN, 900 kN, and 1200 kN, representing the gravity load of the upper storeys were applied at the top of the boundary columns through a force distribution beam. A horizontal cyclic load was then applied at the top of the specimens. The specimen behaviour, envelope curves, axial stress distribution of the infill steel plate, and shear capacity were analyzed. The axial stress distribution and envelope curves were compared with the values predicted using an analytical model available in the literature.

scholarly journals Structure optimization of woven fabric composites for improvement of mechanical properties using a micromechanics model of woven fabric composites and a genetic algorithm

2021 ◽  
Vol 30 ◽  
pp. 263498332110061
Author(s):  
Gunyong Hwang ◽  
Dong Hyun Kim ◽  
Myungsoo Kim
Keyword(s):  
Mechanical Properties ◽  
Genetic Algorithm ◽  
Elastic Modulus ◽  
Fiber Composite ◽  
Woven Fabric ◽  
Cross Sectional ◽  
Micromechanics Model ◽  
Woven Fabric Composites ◽  
Fabric Composites ◽  
Out Of Plane

This research aims to optimize the mechanical properties of woven fabric composites, especially the elastic modulus. A micromechanics model of woven fabric composites was used to obtain the mechanical properties of the fiber composite, and a genetic algorithm (GA) was employed for the optimization tool. The structure of the fabric fiber was expressed using the width, thickness, and wave pattern of the fiber strands in the woven fabric composites. In the GA, the chromosome string consisted of the thickness and width of the fill and warp strands, and the objective function was determined to maximize the elastic modulus of the composite. Numerical analysis showed that the longitudinal mechanical properties of the strands contributed significantly to the overall elastic modulus of the composites because the longitudinal property was notably larger than the transverse property. Therefore, to improve the in-plane elastic modulus, the resulting geometry of the composites possessed large volumes of related strands with large cross-sectional areas and small strand waviness. However, the numerical results of the out-of-plane elastic modulus generated large strand waviness, which contributed to the fiber alignment in the out-of-plane direction. The findings of this research are expected to be an excellent resource for the structural design of woven fabric composites.

scholarly journals Mechanical Characteristics of Fully Grouted and Antiseismic Bolts considering Transverse Deformation in Underground Caverns

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Buyun Yang ◽  
Ming Xiao ◽  
Guoqing Liu ◽  
Juntao Chen
Keyword(s):  
Axial Stress ◽  
Time History ◽  
Beam Theory ◽  
Support Effect ◽  
Transverse Force ◽  
Surrounding Rock ◽  
Axial Deformation ◽  
Transverse Deformation ◽  
Rock Interaction ◽  
Underground Caverns

The load transfer control equations under bolt-surrounding rock interaction are established on the basis of classical beam theory and the trilinear shear slip model. The axial stress and transverse shear force distributions of the anchorage body are obtained by solving the equations. The equivalent forces obtained by the transverse force and axial shear stress of the bolts are applied to rock mass elements to simulate the support effect. A new dynamic algorithm for bolts is proposed in considering of the axial and transverse deformation of the anchorage body. The rationality of the algorithm is verified by comparing with laboratory pullout and shear tests of bolts. A dynamic time-history case study of underground caverns is conducted using this algorithm. Results indicate that (1) the algorithm may reflect the stress and deformation characteristics of bolts during an earthquake; (2) for the antiseismic support effect of the surrounding rock at fault, the bolt algorithm in this study is more valid than the algorithm that considered only the axial deformation of bolts; (3) in the support force of the bolt to the surrounding rock, transverse force is the key to limit fault dislocation and reduce the dynamic damage of the rock at fault.

Generalised Beam Theory for composite beams with longitudinal and transverse partial interaction

2016 ◽  
Vol 22 (10) ◽  
pp. 2011-2039 ◽  
Author(s):  
Gerard Taig ◽  
Gianluca Ranzi
Keyword(s):  
Structural Response ◽  
Beam Theory ◽  
Element Model ◽  
Composite Beams ◽  
Cross Sectional ◽  
Shear Connections ◽  
Dynamic Analyses ◽  
Partial Interaction ◽  
Deformation Modes ◽  
Generalised Beam Theory

This paper presents a Generalised Beam Theory formulation to study the partial interaction behaviour of two-layered prismatic steel–concrete composite beams. The novelty of the proposed approach is in its capacity to handle the deformability of the shear connections at the interface between the slab and steel beam in both the longitudinal and transverse directions in the evaluation of the deformation modes. This method falls within a category of cross-sectional analyses available in the literature for which a suitable set of deformation modes, including conventional, extension and shear, is determined from dynamic analyses of discrete planar frame models representing the cross-section. In this context, the shear connections are modelled using shear deformable spring elements. As a result, the in-plane partial shear interaction behaviour is accounted for in the planar dynamic analysis during the evaluation of the conventional and extension modes, while the longitudinal partial interaction behaviour associated with the shear modes is included in the out-of-plane dynamic analyses. In the case of the conventional modes, the longitudinal slip is accounted for in the post-processing stage where the warping displacements are determined. A numerical example of a composite box girder beam is presented and its structural response investigated for different levels of shear connection stiffness in both the longitudinal and transverse directions. The accuracy of the numerical results is validated against those obtained with a shell finite element model implemented in ABAQUS/Standard software.

scholarly journals Natural Frequency Characteristics of the Beam with Different Cross Sections Considering the Shear Deformation Induced Rotary Inertia

2020 ◽  
Vol 10 (15) ◽  
pp. 5245
Author(s):  
Chunfeng Wan ◽  
Huachen Jiang ◽  
Liyu Xie ◽  
Caiqian Yang ◽  
Youliang Ding ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Cross Sections ◽  
Timoshenko Beam ◽  
High Frequency ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Timoshenko Beam Theory ◽  
Rotary Inertia ◽  
Cross Sectional

Based on the classical Timoshenko beam theory, the rotary inertia caused by shear deformation is further considered and then the equation of motion of the Timoshenko beam theory is modified. The dynamic characteristics of this new model, named the modified Timoshenko beam, have been discussed, and the distortion of natural frequencies of Timoshenko beam is improved, especially at high-frequency bands. The effects of different cross-sectional types on natural frequencies of the modified Timoshenko beam are studied, and corresponding simulations have been conducted. The results demonstrate that the modified Timoshenko beam can successfully be applied to all beams of three given cross sections, i.e., rectangular, rectangular hollow, and circular cross sections, subjected to different boundary conditions. The consequence verifies the validity and necessity of the modification.

Design Framework for Multi-Section Shape Memory Alloy Axial Actuators Considering Material and Geometric Uncertainties

2020 ◽  
Author(s):  
Weilin Guan ◽  
Edwin A. Peraza Hernandez
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
High Energy ◽  
High Energy Density ◽  
Design Framework ◽  
Efficient Design ◽  
Cross Sectional ◽  
Geometric Uncertainties ◽  
In Series ◽  
The Wire

Abstract Shape memory alloys are metallic materials with the capability of performing as high energy density actuators driven by temperature control. This paper presents a design framework for shape memory alloy (SMA) axial actuators composed of multiple wire sections connected in series. The various wire sections forming the actuators can have distinct cross-sectional areas and lengths, which can be modulated to adjust the overall thermomechanical response of the actuator. The design framework aims to find the optimal cross-sectional areas and lengths of the wire sections forming the axial actuator such that its displacement vs. temperature actuation path approximates a target path. Constraints on the length-to-diameter aspect ratio and stress of the wire sections are incorporated. A reduced-order numerical model for the multi-section SMA actuators that allows for efficient design evaluations is derived and implemented. An approach to incorporate uncertainty in the geometry and material parameters of the actuators within the design framework is implemented to allow for the determination of robust actuator designs. A representative application example of the design framework is provided illustrating the benefits of using multiple wire sections in axial actuators to modulate their overall response and approximate a target displacement vs. temperature actuation path.

Modelling of Rotating Twisted Blades as 1D Continuum

2016 ◽  
Vol 821 ◽  
pp. 183-190
Author(s):  
Jan Brůha ◽  
Drahomír Rychecký
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Beam Theory ◽  
Parameter Tuning ◽  
Finite Element Models ◽  
Cross Sectional ◽  
One Dimensional ◽  
Rayleigh Beam ◽  
Twisted Blade ◽  
Sectional Parameters

Presented paper deals with modelling of a twisted blade with rhombic shroud as one-dimensional continuum by means of Rayleigh beam finite elements with varying cross-sectional parameters along the finite elements. The blade is clamped into a rotating rigid disk and the shroud is considered to be a rigid body. Since the finite element models based on the Rayleigh beam theory tend to slightly overestimate natural frequencies and underestimate deflections in comparison with finite element models including shear deformation effects, parameter tuning of the blade is performed.

Antiplane Shear Deformations for Homogeneous and Inhomogeneous Anisotropic Linearly Elastic Solids

1994 ◽  
Vol 61 (1) ◽  
pp. 23-29 ◽  
Author(s):  
C. O. Horgan ◽  
K. L. Miller
Keyword(s):  
Axial Stress ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Antiplane Shear ◽  
Shear Stresses ◽  
Elastic Solids ◽  
Shear Deformations ◽  
End Effects ◽  
Elastic Symmetry ◽  
Cross Sectional

Antiplane shear deformations of a cylindrical body, with a single displacement field parallel to the generators of the cylinder and independent of the axial coordinate, are one of the simplest classes of deformations that solids can undergo. They may be viewed as complementary to the more familiar plane deformations. Antiplane (or longitudinal) shear deformations have been the subject of the considerable recent interest in nonlinear elasticity theory for homogeneous isotropic solids. In contrast, for the linear theory of isotropic elasticity, such deformations are usually not extensively discussed. The purpose of the present paper is to demonstrate that for inhomogeneous anisotropic linearly elastic solids the antiplane shear problem does provide a particularly tractable and illuminating setting within which effects of anisotropy and inhomogeneity may be examined. We consider infinitesimal antiplane shear deformations of an inhomogeneous anisotropic linearly elastic cylinder subject to prescribed surface tractions on its lateral boundary whose only nonzero component is axial and which does not vary in the axial direction. In the absence of body forces, not all arbitrary anisotropic cylinders will sustain an antiplane shear deformation under such tractions. Necessary and sufficient conditions on the elastic moduli are obtained which do allow an antiplane shear. The resulting boundary value problems governing the axial displacement are formulated. The most general elastic symmetry consistent with an antiplane shear is described. There are at most 15 independent elastic coefficients associated with such a material. In general, there is a normal axial stress present, which can be written as a linear combination of the two dominant shear stresses. For a material with the cylindrical cross-section a plane of elastic symmetry (monoclinic, with 13 moduli), the normal stress is no longer present. For homogeneous materials, it is shown how the governing boundary value problem can be transformed to an equivalent isotropic problem for a transformed cross-sectional domain. Applications to the issue of assessing the influence of anisotropy and inhomogeneity on the decay of Saint-Venant end effects are described.

scholarly journals Variational Principles for Multiwalled Carbon Nanotubes Undergoing Vibrations Based on Nonlocal Timoshenko Beam Theory

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Ismail Kucuk ◽  
Ibrahim S. Sadek ◽  
Sarp Adali
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Multiwalled Carbon Nanotubes ◽  
Timoshenko Beam ◽  
Variational Principles ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Small Scale ◽  
Multiwalled Carbon ◽  
Nonlocal Timoshenko Beam Theory

Variational principles are derived for multiwalled carbon nanotubes undergoing linear vibrations using the semi-inverse method with the governing equations based on nonlocal Timoshenko beam theory which takes small scale effects and shear deformation into account. Physical models based on the nonlocal theory approximate the nanoscale phenomenon more accurately than the local theories by taking small scale phenomenon into account. Variational formulation is used to derive the natural and geometric boundary conditions which give a set of coupled boundary conditions in the case of free boundaries which become uncoupled in the case of the local theory. Hamilton's principle applicable to this case is also given.

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