Deformation of a “Rigid” Molecule in Self-Assembled Nanostructures
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A simple spirobifluorene molecule with pseudotetrahedral structure was investigated for its supposed conformational resilience upon adsorption. Through deposition at room temperature of this molecule on a Cu(111) surface and subsequent observation at 5 K with an ultrahigh vacuum scanning tunneling microscope, this "rigidity" upon physisorption is confirmed. However, an unexpected chemisorbed state was also found with the molecules arranged in trimers. The unique coexistence of physisorbed and chemisorbed states on the same substrate is thus demonstrated at the early stage of self-assembly.Keywords:
Physisorption
Rigidity (electromagnetism)
Structural rigidity
Abstract We study structural rigidity for assemblies with mechanical joints. Existing methods identify whether an assembly is structurally rigid by assuming parts are perfectly rigid. Yet, an assembly identified as rigid may not be that “rigid” in practice, and existing methods cannot quantify how rigid an assembly is. We address this limitation by developing a new measure, worst‐case rigidity , to quantify the rigidity of an assembly as the largest possible deformation that the assembly undergoes for arbitrary external loads of fixed magnitude. Computing worst‐case rigidity is non‐trivial due to non‐rigid parts and different joint types. We thus formulate a new computational approach by encoding parts and their connections into a stiffness matrix, in which parts are modeled as deformable objects and joints as soft constraints. Based on this, we formulate worst‐case rigidity analysis as an optimization that seeks the worst‐case deformation of an assembly for arbitrary external loads, and solve the optimization problem via an eigenanalysis. Furthermore, we present methods to optimize the geometry and topology of various assemblies to enhance their rigidity, as guided by our rigidity measure. In the end, we validate our method on a variety of assembly structures with physical experiments and demonstrate its effectiveness by designing and fabricating several structurally rigid assemblies.
Rigidity (electromagnetism)
Structural rigidity
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Rigid origami is examined from the perspective of rigidity theory. First and second order rigidity are defined from local differential analysis of the consistency constraint; while the static rigidity and prestress stability are defined after finding the form of internal force and load. This article will show that first-order or static rigidity implies prestress stability, which implies second-order rigidity, which implies rigidity, but none of these is reversible. Examples are given of rigid origami structures with these different kinds of rigidity. Examining the different aspects of the rigidity of origami might give a novel perspective for the development of new folding patterns, or for the design of origami structures where some rigidity is required.
Rigidity (electromagnetism)
Structural rigidity
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A kind of 3 axle rotary flexible hinge with high axial rigidity has been studied.Principle and method for carrying out analysis by adopting finite element technique on bending rigidity,torsional rigidity and axial rigidity were put forward.Taking these as a base,the finite element analytical calculation on rigidities of each direction of the 3 axle rotary flexible hinge with high axial rigidity was carried out.The quadratic fitting equation of rigidities in each direction of the 3 axle rotary flexible hinge with high axial rigidity that change along with variations of the key structural parameters of flexible hinge was established.The result of study showed that the 3 axle rotary flexible hinge with high axial rigidity possesses not only the equality in bending rigidities of every direction but also possesses rather high axial rigidity,and could realize rotations in the 3 axles.In addition,the maximum fitting error between the quadratic fitting curve with its rigidity value in various directions that varies along with the variation of key structural parameters and the tested curve would not exceed by 3.50%.The quadratic fitting equation of rigidity in various directions that varies along with the changes of key structural parameters of the flexible hinge could predict accurately rigidities in various directions of the flexible hinge.The research works provided a kind of effective method for the development and design of 3 axle rotary flexible hinge with high axial rigidity.
Rigidity (electromagnetism)
Structural rigidity
Flexural rigidity
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With the growing construction of multi-pylon cable-stayed bridges at home and abroad,the numbers of the pylons used for such type of the bridges and the spacing distances among the pylons constantly increase.The way of how to ensure the global rigidity of the bridges becomes a critical issue confronted in development of the structural systems.On the basis of analysis of the structural characteristics and mechanical behavior of the bridges,the factors having influences on the global rigidity of the bridges having 3 pylons,4 pylons and more than 4 pylons are analyzed from three aspects of the rigidity of pylon,stay cable and girder,setting of auxiliary structure and utilization of extradosed bridge.The measures for improving the rigidity of the bridges having been completed and being constructed at home and abroad are compared and summarized and the effective method for improving the rigidity of the bridges having different numbers of the pylons is obtained.The method herewith may provide technical reference for design and construction of the multi-pylon cable-stayed bridges in the future.
Pylon
Rigidity (electromagnetism)
Structural rigidity
Bridge (graph theory)
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Rigidity and flexibility is the basic characteristics of sensor and is the important indexes for quantitatively weighing the relationship between its property and structural parameters in the working space. By applying the theory of mechanisms of parallel robot, a theoretical deduction was carried out on property indexes of 6-dimensional force sensor based on Steward structure. The property indexes of its rigidity and flexibility were defined and analyzed thus provided theoretical basis for the optimization design and engineering application of 6-dimensional force sensor.
Rigidity (electromagnetism)
Structural rigidity
Stewart platform
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Rigidity (electromagnetism)
Structural rigidity
Bar (unit)
Representation
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Rigidity (electromagnetism)
Structural rigidity
Structural Stability
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Non-linear static analysis or pushover analysis is now-a –days generally preferred by many researchers to analyse the non-linear behaviour of the structure. Present study includes the effect of joint rigidity on the behaviour of the structure. A building is modeled with 5 and 10 story and designed for gravity and earthquake resistant loads by considering joint rigidity factor as 0 and 1. The analysis is done in both X and Y directions by using pushover analysis in SAP2000 software. Comparison is made between then capacity curves obtained from designed models of rigidity and non-rigidity models. From the results it is concluded that structure designed using joint rigidity has more strength when compared non-rigid joints.
Rigidity (electromagnetism)
Structural rigidity
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Machine tools is also called mother machine, and it is the essential equipment in all kinds of manufacturing industry up to automobiles, aircraft and the information terminal. As requirements for machining tools, high rigidity and low thermal expansion is important to perform high-precision machining, and having high damping is necessary to realize high-speed machining. In addition, recently weight saving is also required to allow energy saving. However, since high rigidity and light weight is difficult to achieve both, so this study aims to achieve these requirements by optimize machine tool structure through topology optimization. To verify the result of the optimization, create multiple models to compare new models and previous model in the static rigidity and dynamic rigidity. As a result of analysis, it was found that the new model has 5 times stronger static rigidity than previous model and has high dynamic rigidity.
Rigidity (electromagnetism)
Machine tool
Structural rigidity
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For this study, a rigidity test car was designed and manufactured to enable investigation of how non-structural members in the carbody influence the rigidity and vibration characteristics of a commuter-type railway vehicle. Reinforcing beams and pillars designed for easy attachment and removal were installed on the ceiling, the side panels and the floor. The authors performed static load and excitation tests, and the results showed that the non-structural members, as well as the main (outer) body structures, affected the equivalent rigidity, natural frequencies, vibration shapes and response accelerations of the carbody.
Rigidity (electromagnetism)
Structural rigidity
Ceiling (cloud)
Natural frequency
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