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Hinged Beams
Published in A.I. Rusakov, Fundamentals of Structural Mechanics, Dynamics, and Stability, 2020
Virtual displacements are infinitesimal displacements permitted by constraints in a system. Infinitesimal displacements are displacements small enough that, in calculation of required physical values, the errors of analysis may be neglected. The total work done by an assemblage of forces exerted on a system as it moves through a set of virtual displacements is called virtual work.
General Analytical Theory of Super-Structures
Published in Dongzhou Huang, Bo Hu, Concrete Segmental Bridges, 2020
The method of virtual work is based on the principle of virtual work and is an energy method that is based on the principles of conservation of energy, which states that the work done by all the external forces acting on a structure is transformed into internal work or strain energy that is developed when the structure deforms. For more complicated loadings or for more complicated structures, it is often convenient to use energy methods in determining structural displacements. In the principle of virtual work, the total virtual work done by external virtual loads through the displacements due to the real loads is equal to the total strain energy developed by the internal virtual forces through the internal deformations caused by the real loads.
Strain energy and virtual work
Published in A. Ghali, A. M. Neville, T. G. Brown, Structural Analysis, 2017
A. Ghali, A. M. Neville, T. G. Brown
This principle relates a system of forces in equilibrium to a compatible system of displacements in a linear or nonlinear structure. The name of the principle is derived from the fact that a fictitious (virtual) system of forces in equilibrium or of small virtual displacements is applied to the structure and related to the actual displacements or actual forces respectively. Any system of virtual forces or displacements can be used, but it is necessary that the condition of equilibrium of the virtual forces or of compatibility of the virtual displacements be satisfied. This means that the virtual displacements can be any geometrically possible infinitesimal displacements: they must be continuous within the structure boundary and must satisfy the boundary conditions. With an appropriate choice of virtual forces or displacements, the principle of virtual work can be used to compute displacements or forces.
Dynamic analysis of an over-constrained parallel mechanism with the principle of virtual work
Published in Mathematical and Computer Modelling of Dynamical Systems, 2021
Miao Chen, Qing Zhang, Yunfei Ge, Xianrong Qin, Yuantao Sun
To obtain an accurate dynamic formulation, this paper presents a general procedure to conduct the complete dynamics analysis of the over-constrained 2UPR-RRU parallel mechanism. The kinematic analysis was performed which included the position, velocity, and acceleration problems and Jacobian matrices, the complete dynamic model with friction model was developed by the principle of virtual work. Theoretical required active forces by actuators are finally obtained to follow the proposed trajectory of the moving platform. Simulations and comparisons with a Simscape virtual prototype and a rigid-flexible coupling dynamic model showed the correctness of the developed theoretical dynamic model. Without considering the analysis of complex internal forces, the virtual work method is more computationally efficient. This work paves the way for the control strategy research of 2UPR-RRU parallel mechanism in the future. The methodology can also be used for dynamic analysis of similar parallel mechanisms.
An experimentally validated numerical method for investigating the air blast response of basalt composite plates
Published in Mechanics of Advanced Materials and Structures, 2020
Sedat Süsler, Hasan Kurtaran, Halit S. Türkmen, Zafer Kazancı, Valentina Lopresto
FSDT is used to take into account transverse shear effect and von Karman nonlinear strain–displacement relationships are used to take into account large deflection effect. Virtual work principle is used to derive the dynamic equations of motion. Additionally, a commercial finite element solver, ANSYS, is also used to model the dynamic behaviour of basalt plates subjected to blast load. GDQ and ANSYS results are compared with experimental results. It is found that there is a good agreement between the FEM, GDQ, and experimental results for the dynamic behaviour of blast loaded basalt composite plates which have different stacking sequences and fiber orientations.
Exact shell solutions for conical springs. II. Radial cylindric curb
Published in Mechanics Based Design of Structures and Machines, 2023
The radius (30) of inversion center is given by Almen and Laszlo formula. According to the principle of virtual work, the external virtual work is equal to internal virtual work when equilibrated forces and stresses undergo unrelated but consistent displacements and strains. The necessary stationarity condition with respect to delivers the circumferential moment for the spring with gliding edges: