scholarly journals Stability of trusses by graphic statics

2021 ◽  
Vol 8 (6) ◽  
pp. 201970
Author(s):  
Allan McRobie ◽  
Cameron Millar ◽  
William F. Baker
Keyword(s):  
Axial Force ◽  
Graphical Representation ◽  
Graphical Method ◽  
Three Dimensional ◽  
Weighted Sum ◽  
Two Dimensional ◽  
Rotational Stiffness ◽  
Graphic Statics ◽  
Out Of Plane ◽  
Pinned Joints

This paper presents a graphical method for determining the linearized stiffness and stability of prestressed trusses consisting of rigid bars connected at pinned joints and which possess kinematic freedoms. Key to the construction are the rectangular areas which combine the reciprocal form and force diagrams in the unified Maxwell–Minkowski diagram. The area of each such rectangle is the product of the bar tension and the bar length, and this corresponds to the rotational stiffness of the bar that arises due to the axial force that it carries. The prestress stability of any kinematic freedom may then be assessed using a weighted sum of these areas. The method is generalized to describe the out-of-plane stability of two-dimensional trusses, and to describe three-dimensional trusses in general. The paper also gives a graphical representation of the ‘product forces’ that were introduced by Pellegrino and Calladine to describe the prestress stability of trusses.

Can a three-dimensional composite really provide better mechanical performance compared to two-dimensional composite under compressive loading?

2018 ◽  
Vol 38 (2) ◽  
pp. 49-61 ◽  
Author(s):  
M Tarfaoui ◽  
M Nachtane
Keyword(s):  
Mechanical Performance ◽  
Split Hopkinson Pressure Bar ◽  
Compressive Loading ◽  
Three Dimensional ◽  
Woven Composites ◽  
Two Dimensional ◽  
Hopkinson Pressure Bar ◽  
Out Of Plane ◽  
Split Hopkinson ◽  
Pressure Bar

A series of split Hopkinson pressure bar tests on two-dimensional and three-dimensional woven composites were presented in order to obtain a reliable comparison between the two types of composites and the effect of the z-yarns along the third direction. These tests were done along different configurations: in-plane and out-of-plane compression test. For the three-dimensional woven composite, two different configurations were studied: compression responses along to the stitched direction and orthogonal to the stitched direction. It was found that three-dimensional woven composites exhibit an increase in strength for both: in-plane and out-of-plane tests.

Piezoelectricity in Monolayers and Bilayers of Inorganic Two-Dimensional Crystals

2013 ◽  
Vol 1556 ◽  
Author(s):  
Karel-Alexander N. Duerloo ◽  
Mitchell T. Ong ◽  
Evan J. Reed
Keyword(s):  
Density Functional ◽  
Electromechanical Coupling ◽  
Three Dimensional ◽  
Single Layer ◽  
Elastic Model ◽  
Two Dimensional ◽  
Functional Theory ◽  
Symmetry Properties ◽  
Electromechanical Effects ◽  
Out Of Plane

ABSTRACTThe symmetry properties of many inorganic two-dimensional monolayer crystals make them piezoelectric, whereas their three-dimensional parent crystals are not. The emergence of piezoelectricity in the single-layer limit points toward intriguing electromechanical effects and applications in the single- or few-layer regime. We use density functional theory to calculate the piezoelectric coefficients of BN, MoS2, MoSe2, MoTe2, WS2, WSe2 and WTe2. These coefficients are found to be comparable to, and in some cases greater than those of commonly used wurtzite piezoelectrics. The centrosymmetry of a BN bilayer prevents a piezoelectric effect for this structure. However, by developing an elastic model, we find that the bilayer exhibits an unusual electromechanical coupling to the curvature, similar to that of a bimorph. A BN bilayer is found to amplify the constituent monolayers’ in-plane piezoelectric displacements by factors on the order of 103-104 into out-of plane deflections.

Automated Composite Fabric Layup for Wind Turbine Blades

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Siqi Zhu ◽  
Corey J. Magnussen ◽  
Emily L. Judd ◽  
Matthew C. Frank ◽  
Frank E. Peters
Keyword(s):  
Wind Turbine ◽  
Plane Deformation ◽  
Turbine Blades ◽  
Three Dimensional ◽  
3D Models ◽  
New Method ◽  
Two Dimensional ◽  
Wind Turbine Blades ◽  
Out Of Plane ◽  
Fiberglass Fabric

This work presents an automated fabric layup solution based on a new method to deform fiberglass fabric, referred to as shifting, for the layup of noncrimp fabric (NCF) plies. The shifting method is intended for fabric with tows only in 0 deg (warp) and 90 deg (weft) directions, where the fabric is sequentially constrained and then rotated through a deformation angle to approximate curvature. Shifting is conducted in a two-dimensional (2D) plane, making the process easy to control and automate, but can be applied for fabric placement in three-dimensional (3D) models, either directly or after a ply kitting process and then manually placed. Preliminary tests have been conducted to evaluate the physical plausibility of the shifting method. Layup tests show that shifting can deposit fabric accurately and repeatedly while avoiding out-of-plane deformation.

scholarly journals Optical detection of the susceptibility tensor in two-dimensional crystals

2021 ◽  
Author(s):  
Michele Merano ◽  
Zhemi Xu ◽  
Davide Ferraro ◽  
Annamaria Zaltron ◽  
Nicola Galvanetto ◽  
...  
Keyword(s):  
Plane Surface ◽  
Three Dimensional ◽  
Single Layer ◽  
Optical Response ◽  
Optical Measurements ◽  
Two Dimensional ◽  
Reliable Determination ◽  
Susceptibility Tensor ◽  
Two Dimensional Materials ◽  
Out Of Plane

Abstract The out-of-plane optical constants of two-dimensional materials have proven to be experimentally elusive. Owing to the reduced dimensionality of a monolayer, optical measurements have limited sensitivity to these properties, which are hidden by the optical response of the substrate. Therefore, there remains an absence of scientific consensus on how to correctly model these materials. Theoretical descriptions span from isotropic three-dimensional slabs to two-dimensional surface currents with a null out-of-plane surface susceptibility. Here we perform a smoking gun experiment on the optical response of a single-layer two-dimensional crystal that addresses these problems. We successfully remove the substrate contribution to the optical response of these materials by a step deposition of a monolayer crystal inside a thick polydimethylsiloxane prism. This allows for a reliable determination of both the in-plane and the out-of-plane components of the monolayer surface susceptibility tensor. Our results prescribe one clear theoretical model for these types of material. This work creates opportunities for a precise characterization of the optical properties of two-dimensional crystals in all the optical domains such as the nonlinear response, surface wave phenomena or magneto-optical Kerr effect. Our assay will be relevant to future progresses in photonics and optoelectronics with 2D materials.

scholarly journals Two - Dimensional Finite Element Analysis of Composite Patch Repairs Using Shell Laminate Elements

2003 ◽  
Vol 12 (2) ◽  
pp. 096369350301200
Author(s):  
George J Tsamasphyros ◽  
George N Kanderakis ◽  
Nikos K Furnarakis ◽  
Zaira P Marioli-Riga
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Element Analysis ◽  
Composite Patch ◽  
Out Of Plane ◽  
Dimensional Finite Element ◽  
Patch Repairs ◽  
Three Dimensional Finite Element

A host of one and two-sided composite patch reinforcements of metallic structures with different patch thickness were considered, in order to compare two-dimensional finite element analysis using shell laminate elements with three-dimensional finite element analysis. In order to verify the accuracy of this approach a parametric study has been performed and the 2D results were compared to the outcome of the corresponding three-dimensional finite element analysis, which accuracy has been experimentally verified in previous works. It was found that for the case of two-sided reinforcement the results obtained by the two methods were in very good agreement. For the case of one-sided reinforcement some deviation of the results of two-dimensional analysis has been observed, which was due to the tendency of the structure for out-of-plane bending, resulting from the bonding of a reinforcing patch to only one face of the structure. According to the results of this parametric study and since most aircraft structures are constrained against local out-of-plane bending (e.g. aircraft skins through stringers) two-dimensional finite elements analysis using shell laminate elements is proposed as an accurate and easy to use analysis tool for the design of both one and two-sided composite patch repairs of relatively simple structures.

A Comparison Between the Accuracy of Two-Dimensional and Three-Dimensional Strain Measurements

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Niranjan Desai ◽  
Joel Poling ◽  
Gregor Fischer ◽  
Christos Georgakis
Keyword(s):  
Structural Damage ◽  
Measurement Techniques ◽  
Three Dimensional ◽  
Image Correlation ◽  
3D Measurement ◽  
Two Dimensional ◽  
Strain Measurements ◽  
Out Of Plane ◽  
2D System ◽  
Plane Displacement

This investigation determined the effect of specimen out-of-plane movement on the accuracy of strain measurement made applying two-dimensional (2D) and three-dimensional (3D) measurement approaches using the representative, state-of-the-art digital image correlation (DIC)-based tool ARAMIS. DIC techniques can be used in structural health monitoring (SHM) by measuring structural strains and correlating them to structural damage. This study was motivated by initially undetected damage at low strains in connections of a real-world bridge, whose detection would have prevented its propagation, resulting in lower repair costs. This study builds upon an initial investigation that concluded that out-of-plane specimen movement results in noise in DIC-based strain measurements. The effect of specimen out-of-plane displacement on the accuracy of strain measurements using the 2D and 3D measurement techniques was determined over a range of strain values and specimen out-of-plane displacements. Based upon the results of this study, the 2D system could measure strains as camera focus was being lost, and the effect of the loss of focus became apparent at 1.0 mm beam out-of-plane displacement while measuring strain of the order of magnitude of approximately 0.12%. The corresponding results for the 3D system demonstrate that the beam out-of-plane displacement begins to affect the accuracy of the strain measurements at approximately 0.025% strain for all magnitudes of out-of-plane displacement, and the 3D ARAMIS system can make accurate strain measurements at up to 2.5 mm amplitude at this strain. Finally, based upon the magnitudes of strain and out-of-plane displacement amplitudes that typically occur in real steel bridges, it is advisable to use the 3D system for SHM of stiff structures instead of the 2D system.

Graphical representation of stereochemical configuration (IUPAC Recommendations 2006)

2006 ◽  
Vol 78 (10) ◽  
pp. 1897-1970 ◽  
Author(s):  
Jonathan Brecher
Keyword(s):  
Graphical Representation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Wide Audience ◽  
Stereochemical Configuration ◽  
Stereogenic Centers ◽  
Relationship Of ◽  
Stereogenic Center ◽  
The Relationship

Stereochemical configuration is determined by the relationship of atoms in three-dimensional space, yet remains most commonly represented in two-dimensional media such as printed publications or computer screens. Recommendations are provided for the display of three-dimensional stereochemical information in two-dimensional diagrams in ways that avoid ambiguity and are likely to be understood correctly by all viewers. Examples are provided for all types of stereochemical configuration, with explanation of which styles are preferred and which should be avoided. Principal recommendations include:Know your audience: Diagrams that have a wide audience should be drawn as simply as possible.Avoid ambiguous drawing styles.Avoid the use of perspective diagrams and class-specific drawing styles (Fischer projections, Haworth projections, etc.) when structures are to be interpreted by computers.Use solid wedges to indicate bonds that project above the plane of the paper and hashed wedges to indicate bonds that project below the plane of the paper; in both cases, the bonds must be oriented with the narrow end at the stereogenic center.Avoid connecting stereogenic centers with a stereobond.

scholarly journals Analytical graphic statics

2021 ◽  
pp. 095605992110016
Author(s):  
Tamás Baranyai
Keyword(s):  
Stress Function ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Linear Functionals ◽  
The Past ◽  
Force Diagram ◽  
Graphic Statics ◽  
Reciprocal Diagrams ◽  
Force Systems ◽  
Stress Functions

Graphic statics is undergoing a renaissance, with computerized visual representation becoming both easier and more spectacular as time passes. While methods of the past are revived, little emphasis has been placed on studying the mathematics behind these methods. Due to the considerable advances of our mathematical understanding since the birth of graphic statics, we can learn a lot by examining these old methods from a more modern viewpoint. As such, this work shows the mathematical fabric joining different aspects of graphic statics, like dualities, reciprocal diagrams, and discontinuous stress functions. This is done by introducing a new, three dimensional force diagram (containing the old two dimensional force diagram) depicting the three dimensional equilibrium of planar force systems. A corresponding three dimensional “form diagram” (dual diagram) is introduced, in which forces are treated as linear functionals (dual vectors). It is shown that the polyhedral stress function introduced by Maxwell is in fact a linear combination of these functionals; and the projective dualities connecting these three dimensional diagrams are also explained.

A Graphical Method for Determining Truss Stability

2020 ◽  
Vol 61 (4) ◽  
pp. 285-295
Author(s):  
Cameron Millar ◽  
Allan McRobie ◽  
William Baker
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Graphical Method ◽  
Weighted Sum ◽  
The Finite Element Method ◽  
Significant Development ◽  
Graphic Statics ◽  
Hands On ◽  
The Stability ◽  
Structural Mechanisms

Graphic statics has been used for over 150 years, having been pioneered by the likes of Maxwell, Cremona, Culmann and Rankine, and has recently seen a resurgence in popularity because of its use in design. However, it is only concerned with equilibrium; as any engineer will testify, whilst equilibrium is necessary, it is not sufficient and stability must also be obtained. This paper develops a novel graphical method for determining the stability and stiffness of prestressable structures. By considering the weighted sum of the Maxwell-Minkowski diagram, the stiffness and stability of the structural mechanisms can be determined. This work extends to cover structures with multiple mechanisms and has been compared to results obtained through experimentation and the finite element method. Furthermore, it extends the work on stiffness to provide a graphical method to estimate the natural frequency of a truss. Whilst this method accurately determines the stiffness of structures, it represents a significant development in the field of graphic statics as it allows an engineer to 'eye-ball' the stability of a given truss. Engineers can also manipulate the form and force diagrams, as desired, to adjust the stiffness of their structure accordingly, whilst being able to visualise the process. Much of the previous work in this area relies heavily upon large matrices, while this method allows a more intimate and hands-on alternative.

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