scholarly journals On Symmetrical Deformation of Toroidal Shell with Circular Cross-Section

2020 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
High Performance ◽  
Circular Cross Section ◽  
Gauss Curvature ◽  
Toroidal Shell ◽  
Numerical Comparison ◽  
Symmetrical Deformation ◽  
Deformation Equation ◽  
Bending Capacity ◽  
Heun’S Equation ◽  
Toroidal Shells

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, the symmetrical deformation equation of elastic toroidal shells is successfully transferred into a well-known equation, namely Heun's equation of ordinary differential equation, whose exact solution is obtained in terms of Heun's functions. The computation of the problem can be carried out by symbolic software that is able to with the Heun's function, such as Maple. The Gauss curvature of the elastic toroidal shells shows that the internal portion of the toroidal shells has better bending capacity than the outer portion, which might be useful for the design of metamaterials with toroidal shells cells. Through numerical comparison study, the mechanics of elastic toroidal shells is sensitive to the radius ratio. By slightly adjustment of the ratio might get a desired high performance shell structure.

scholarly journals On Symmetrical Deformation of Toroidal Shell with Circular Cross-Section

2020 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Differential Equation ◽  
Cross Section ◽  
Circular Cross Section ◽  
Gauss Curvature ◽  
Toroidal Shell ◽  
Symmetrical Deformation ◽  
Deformation Equation ◽  
Bending Capacity ◽  
Heun’S Equation ◽  
Geometric Study

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, the complicated deformation equation of toroidal shell is successfully transferred into a well-known equation, namely Heun's equation of ordinary differential equation, whose exact solution is obtained in terms of Heun's functions. The computation of the problem can be carried out by symbolic software that is able to with the Heun's function, such as Maple. The geometric study of the Gauss curvature shows that the internal portion of the toroidal shell has better bending capacity than the outer portion, which might be useful for the design of metamaterials with toroidal shell cells.

scholarly journals Small Symmetrical Deformation of Thin Torus with Circular Cross-Section

2021 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Cross Section ◽  
Circular Cross Section ◽  
Complex Form ◽  
Real Form ◽  
Element Analysis ◽  
Numerical Studies ◽  
Ode System ◽  
Symmetrical Deformation

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, a complex-form ordinary differential equation (ODE) for the small symmetrical deformation of an elastic torus is successfully transformed into the well-known Heun's ODE, whose exact solution is obtained in terms of Heun's functions. To overcome the computational difficulties of the complex-form ODE in dealing with boundary conditions, a real-form ODE system is proposed. A general code of numerical solution of the real-form ODE is written by using Maple. Some numerical studies are carried out and verified by both finite element analysis and H. Reissner's formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell.

scholarly journals Experimental and Numerical Investigation on Shear Retrofitting of RC Beams by Prefabricated UHPFRC Sheets

2016 ◽  
Vol 2 (5) ◽  
pp. 168-179
Author(s):  
Kian Aghani ◽  
Hassan Afshin
Keyword(s):  
Reinforced Concrete ◽  
High Performance ◽  
Fem Analysis ◽  
Fiber Reinforced Concrete ◽  
Bending Test ◽  
Rc Beams ◽  
Fiber Reinforced ◽  
Externally Bonded ◽  
High Performance Fiber ◽  
Bending Capacity

Different methods are used for retrofitting RC members. One of the new methods in this field is using externally bonded fiber-reinforced Concrete (FRC) sheets in order to increase RC member’s shear and flexural strength. In this study, applicability of ultra-high performance fiber-reinforced concrete sheets in shear and flexural retrofitting of RC beams was investigated. In total, eight RC beams (dimensions 10×20×150 cm) with two different bending capacity and lack of shear strength were used and were tested in 3-points bending test. Of these, four were control beams and four were retrofitted with laterally bonded UHPFRC sheets. Dimensions of the sheets used for retrofitting were (3×15×126 cm). Also FEM analysis was used to model the effect of The method. the results show that this method can be well used for retrofitting RC beams. In this method the way of connecting sheets to beam’s surfaces has a fundamental role in behavior of retrofitted beams.

Free Vibration Analysis of an Inflated Toroidal Shell

2002 ◽  
Vol 124 (3) ◽  
pp. 387-396 ◽  
Author(s):  
Akhilesh K. Jha ◽  
Daniel J. Inman ◽  
Raymond H. Plaut
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Free Vibration Analysis ◽  
Longitudinal Direction ◽  
Variable Coefficients ◽  
Mode Shapes ◽  
Toroidal Shell

Free vibration analysis of a free inflated torus of circular cross-section is presented. The shell theory of Sanders, including the effect of pressure, is used in formulating the governing equations. These partial differential equations are reduced to ordinary differential equations with variable coefficients using complete waves in the form of trigonometric functions in the longitudinal direction. The assumed mode shapes are divided into symmetric and antisymmetric groups, each given by a Fourier series in the meridional coordinate. The solutions (natural frequencies and mode shapes) are obtained using Galerkin’s method and verified with published results. The natural frequencies are also obtained for a circular cylinder with shear diaphragm boundary condition as a special case of the toroidal shell. Finally, the effects of aspect ratio, pressure, and thickness on the natural frequencies of the inflated torus are studied.

Edge Influence Coefficients for Toroidal Shells of Negative Gaussian Curvature

1960 ◽  
Vol 82 (1) ◽  
pp. 69-75 ◽  
Author(s):  
G. D. Galletly
Keyword(s):  
Gaussian Curvature ◽  
Constant Thickness ◽  
Toroidal Shell ◽  
Uniform Pressure ◽  
Simple Manner ◽  
Negative Gaussian Curvature ◽  
Influence Coefficients ◽  
Bending Loads ◽  
Edge Influence ◽  
Toroidal Shells

Continuing the work presented in reference [1], the present paper gives additional tables for the edge deformations of constant-thickness toroidal shells subject to edge bending loads and uniform pressure. The two papers together thus cover a wide variety of toroidal shell geometries and enable a designer to calculate in a simple manner the edge moments and shears at toroidal shell junctions.

Experimental and numerical investigation of steel–ultra-high-performance concrete continuous composite beam behavior

2020 ◽  
Vol 23 (10) ◽  
pp. 2220-2236
Author(s):  
Haolei Wang ◽  
Tao Sun ◽  
Chen Tang ◽  
Jiejun Wang
Keyword(s):  
Numerical Model ◽  
Composite Beam ◽  
High Performance ◽  
High Performance Concrete ◽  
Concrete Slab ◽  
Plate Thickness ◽  
Bottom Plate ◽  
Ultra High Performance Concrete ◽  
Plate Height ◽  
Bending Capacity

This article proposes a new kind of continuous composite beam that consists of steel box-girder and ultra-high-performance concrete waffle slab. The ultra-high-performance concrete helps increase the ultimate capacity and span of structure while reducing the risk of cracking that occurs with ordinary concrete. In order to investigate the mechanical properties of this new type of composite structure, two scaled specimens were designed and tested. One was a steel–ultra-high-performance concrete continuous composite beam, whereas the other, as a control specimen, was a prestressed steel-concrete continuous composite beam. The test results indicate that the bending capacity of steel–ultra-high-performance concrete continuous composite beam is 1.2 times that of steel-concrete continuous composite beam; the cracking strength of steel–ultra-high-performance concrete continuous composite beam is larger than 20 MPa, much higher than the conventional one; the crack development pattern of steel–ultra-high-performance concrete continuous composite beam has its own characteristics, and the cracks appeared in ultra-high-performance concrete slab dominated by micro-cracks with smaller length are numerous and intensive. A finite element model was developed to predict the behavior of steel–ultra-high-performance concrete continuous composite beam. Comparing the numerical and experimental results indicates that, generally, the numerical model can simulate the structural behavior of steel–ultra-high-performance concrete continuous composite beam reasonably. Based on the numerical model, a series of parameter analyses were performed, which indicate that the strength grade of steel, web, and bottom plate thickness play an important role in improving the bending capacity of steel–ultra-high-performance concrete continuous composite beam; the axial tensile strength of ultra-high-performance concrete, rib, and top plate height of ultra-high-performance concrete slab can enhance the bending capacity to a certain extent.

Edge Influence Coefficients for Toroidal Shells of Positive Gaussian Curvature

1960 ◽  
Vol 82 (1) ◽  
pp. 60-68 ◽  
Author(s):  
G. D. Galletly
Keyword(s):  
Gaussian Curvature ◽  
Constant Thickness ◽  
Toroidal Shell ◽  
Uniform Pressure ◽  
Dimensionless Form ◽  
Positive Gaussian Curvature ◽  
Influence Coefficients ◽  
Bending Loads ◽  
Edge Influence ◽  
Toroidal Shells

Tables are given for the edge deformations of constant-thickness toroidal shells subject to uniform pressure and edge bending loads. Over one hundred different shell geometries were investigated and the results are presented in dimensionless form. Possession of these coefficients, which were obtained on a digital computer, means that a rapid and accurate formulation of the compatibility equations at toroidal shell junctions is now possible.

A Finite Strip for the Vibration Analysis of Rotating Toroidal Shell Under Internal Pressure

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Ivo Senjanović ◽  
Ivan Áatipović ◽  
Neven Alujević ◽  
Damjan Čakmak ◽  
Nikola Vladimir
Keyword(s):  
Internal Pressure ◽  
Cross Sections ◽  
Stiffness Matrix ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Toroidal Shell ◽  
Beam Shape ◽  
Finite Strip ◽  
Finite Strip Method ◽  
Toroidal Shells

In this paper, a finite strip for vibration analysis of rotating toroidal shells subjected to internal pressure is developed. The expressions for strain and kinetic energies are formulated in a previous paper in which vibrations of a toroidal shell with a closed cross section are analyzed using the Rayleigh–Ritz method (RRM) and Fourier series. In this paper, however, the variation of displacements u, v, and w with the meridional coordinate is modeled through a discretization with a number of finite strips. The variation of the displacements with the circumferential coordinate is taken into account exactly by using simple sine and cosine functions of the circumferential coordinate. A unique argument nφ+ω t is used in order to be able to capture traveling modes due to the shell rotation. The finite strip properties, i.e., the stiffness matrix, the geometric stiffness matrix, and the mass matrices, are defined by employing bar and beam shape functions, and by minimizing the strain and kinetic energies. In order to improve the convergence of the results, also a strip of a higher-order is developed. The application of the finite strip method is illustrated in cases of toroidal shells with closed and open cross sections. The obtained results are compared with those determined by the RRM and the finite element method (FEM).

Vibration Control of Toroidal Shells With Parallel and Diagonal Piezoelectric Actuators

2003 ◽  
Vol 125 (2) ◽  
pp. 171-176 ◽  
Author(s):  
H. S. Tzou ◽  
D. W. Wang
Keyword(s):  
Elastic Shell ◽  
Piezoelectric Sensor ◽  
Analysis Data ◽  
Effective Control ◽  
Toroidal Shell ◽  
Published Data ◽  
System Matrix ◽  
Sensor Actuator ◽  
Parallel Configuration ◽  
Toroidal Shells

Effective control of toroidal shells, e.g., cooling tubes, space colonies, inflatable space structures, etc., enhances their operational precision, accuracy, and reliability. Dynamics and control effectiveness of toroidal shell panels laminated with distributed piezoelectric sensor/actuator layers are investigated in this study. Mathematical model and finite element formulations of piezo(electric)-elastic shell structures are presented. Element and system matrix equations of the piezoelastic shell structronic (sensor/actuator/structure/control) system are defined and the system equations reveal the coupling of mechanical and electric (or control) fields. Free vibration analyses of two toroidal shells are investigated and compared favorably with published data. Two sensor/actuator configurations based on identical sensor/actuator sizes, namely the parallel configuration and the diagonal configuration, laminated on the toroidal shell are investigated and analysis data suggest that the diagonal configuration provides better control effects, as compared with the parallel configuration. The parallel configuration is ineffective to anti-symmetrical modes; the diagonal configuration is effective to most natural modes and ineffective to quad-anti-symmetrical modes with respect to the panel center.

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