THREE-DIMENSIONAL ANALYSIS OF THICK PLATES BY MLS-RITZ METHOD

2008 ◽  
Vol 08 (01) ◽  
pp. 77-101 ◽  
Author(s):  
L. ZHOU ◽  
W. X. ZHENG
Keyword(s):  
Mixed Boundary ◽  
Ritz Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Least Square ◽  
3D Analysis ◽  
Displacement Fields ◽  
Linear Elasticity Theory ◽  
Thick Plates ◽  
Moving Least Square

This paper presents a three-dimensional (3D) moving least-square Ritz (MLS-Ritz) formulation for the free vibration analysis of homogeneous elastic thick plates with mixed boundary constraints. The analysis is based on the linear elasticity theory. The Ritz trial functions are established through the moving least-square technique for the displacement fields of the plates. Vibration frequencies for thick square plates and right-angled isosceles triangular plates are obtained by the MLS-Ritz method. The reliability and accuracy of the presented method are examined by extensive convergence and comparison studies and it is established herein that the MLS-Ritz method is a powerful and effective numerical method for the 3D analysis of thick plates.

Three-Dimensional Vibration Analysis of Twisted Cylinder With Sectorial Cross Section

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
D. Zhou ◽  
S. H. Lo
Keyword(s):  
Cross Section ◽  
Chebyshev Polynomial ◽  
Numerical Solutions ◽  
Twist Angle ◽  
Ritz Method ◽  
Three Dimensional ◽  
Cylindrical Domain ◽  
Linear Elasticity Theory ◽  
Boundary Functions ◽  
Polynomial Series

The three-dimensional (3D) free vibration of twisted cylinders with sectorial cross section or a radial crack through the height of the cylinder is studied by means of the Chebyshev–Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. A simple coordinate transformation is applied to map the twisted cylindrical domain into a normal cylindrical domain. The product of a triplicate Chebyshev polynomial series along with properly defined boundary functions is selected as the admissible functions. An eigenvalue matrix equation can be conveniently derived through a minimization process by the Rayleigh–Ritz method. The boundary functions are devised in such a way that the geometric boundary conditions of the cylinder are automatically satisfied. The excellent property of Chebyshev polynomial series ensures robustness and rapid convergence of the numerical computations. The present study provides a full vibration spectrum for thick twisted cylinders with sectorial cross section, which could not be determined by 1D or 2D models. Highly accurate results presented for the first time are systematically produced, which can serve as a benchmark to calibrate other numerical solutions for twisted cylinders with sectorial cross section. The effects of height-to-radius ratio and twist angle on frequency parameters of cylinders with different subtended angles in the sectorial cross section are discussed in detail.

scholarly journals Modeling technology of curved surface development for puffer fish

2020 ◽  
Vol 12 (4) ◽  
pp. 168781402091602
Author(s):  
Honggen Zhou ◽  
Jie Cui ◽  
Guizhong Tian ◽  
Yesheng Zhu ◽  
Changfeng Jia
Keyword(s):  
Three Dimensional ◽  
Least Square ◽  
Curved Surface ◽  
B Spline ◽  
Implicit Equation ◽  
Moving Least Square ◽  
Average Value ◽  
Modeling Technology ◽  
Surface Development ◽  
Puffer Fish

The drag reduction mechanism of puffer epidermis was closely related to its real geometry. In order to solve the modeling problem of epidermal spines on the puffer surface, a modeling method for the expansion of puffer shape was proposed. The three-dimensional scanning and non-uniform rational B-spline surface modeling technology was used to reconstruct the puffer model. According to the curvature characteristics, the surface mathematical equations including exponential, logarithmic, and sinusoidal functions were established based on the multinomial function. The surface was generated by a mathematical equation, and the surface was divided into several non-uniform rational B-spline patches according to curvature. After discretization, the point cloud Gaussian curvature and average value were calculated based on the implicit equation of moving least square surface, and whether the surface is approximately extensible or not was judged. Finally, the puffer surface was divided into 46 curved patches. In this article, the surface expansion algorithm gave priority to ensure the area unchanged, and four feature surfaces were selected according to the epidermal spines arrangement of the puffer surface. The results showed that the technique can simply and efficiently unfold the curved surface of the puffer fish, thus the mapping relationship between the epidermal spines on the surface and the plane was determined, which established a foundation for the accurate arrangement and modeling of the epidermal spines on the surface.

Three-Dimensional Vibrations of Twisted Cantilevered Parallelepipeds

1986 ◽  
Vol 53 (3) ◽  
pp. 614-618 ◽  
Author(s):  
A. Leissa ◽  
K. I. Jacob
Keyword(s):  
Finite Element ◽  
Twist Angle ◽  
Ritz Method ◽  
Three Dimensional ◽  
Algebraic Polynomials ◽  
Thick Plates ◽  
Cantilevered Beams ◽  
Element Theory

A large number of references dealing with the vibrations of twisted, cantilevered beams and plates exist in the literature. These works show considerable disagreement concerning the effect of twist angle upon frequencies. The present work is the first three-dimensional study of the problem. Displacement components are assumed in the form of algebraic polynomials which satisfy the fixed face conditions exactly, and which are mathematically complete. The Ritz method is then applied. Accurate frequencies are calculated for twisted thick plates and are compared with ones obtained recently by others using beam, shell, and finite element theory.

3-D Free Vibration Analysis of Functionally Graded Thick Circular and Annular Plates on Elastic Foundation

2010 ◽  
Author(s):  
Vahid Tajeddini ◽  
Abdolreza Ohadi ◽  
Mojtaba Sadighi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Small Strain ◽  
Functionally Graded ◽  
Different Boundary Conditions ◽  
Fg Plates

This paper describes a study of three-dimensional free vibration analysis of thick circular and annular functionally graded (FG) plates resting on Pasternak foundation. The formulation is based on the linear, small strain and exact elasticity theory. Plates with different boundary conditions are considered and the material properties of the FG plate are assumed to vary continuously through the thickness according to power law. The kinematic and the potential energy of the plate-foundation system are formulated and the polynomial-Ritz method is used to solve the eigenvalue problem. Convergence and comparison studies are done to demonstrate the correctness and accuracy of the present method. With respect to geometric parameters, elastic coefficients of foundation and different boundary conditions some new results are reported which maybe used as a benchmark solution for future researches.

Free Vibration Analysis of a Fiber Reinforced Mindlin Plate by Using Ritz Method

2011 ◽  
Vol 110-116 ◽  
pp. 350-356
Author(s):  
S.H. Hosseini Hashemi ◽  
S. Fazeli
Keyword(s):  
Free Vibration ◽  
Analytical Solutions ◽  
Fiber Orientation ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Fiber Reinforced ◽  
Displacement Fields

In this paper the free vibration analysis of a fiber reinforced mindlin plate is presented.energy method based on the ritz method is used to obtain natural frequencies of the plate. Displacement fields of the plate are postulated by trigonometric series function. depending on the arrangement and orientation of the fibers, mindlin plate is assumed to be orthotropic or monoclinic.this analysis is useful to study the mechanical behavior of an angle ply lamina and effect of fiber orientation on the frequency response of the plate.the analysis can be extended for the laminates where the analytical solutions are not available. Finally the results are compared with those reported in the literature.

Square Cracks in Three-Dimensional Transversely Isotropic Solids

2012 ◽  
Vol 487 ◽  
pp. 617-621
Author(s):  
Ya Dong Bian ◽  
Yu Zhou Sun
Keyword(s):  
Crack Opening ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Boundary Integral ◽  
Least Square ◽  
Weight Functions ◽  
Opening Displacement ◽  
Moving Least Square ◽  
Moving Least Square Approximation ◽  
Fracture Damage

This paper presents a study for the square crack in a three-dimensional infinite transversely isotropic medium, which can model the fracture damage of rock that displays transversely isotropic behavior. The study is based on a newly derived boundary integral equation. To carry out the numerical simulation, the crack opening displacement is first expressed as the product of the weight functions and the characteristic terms, and the unknown weight is approximated with the moving least-square approximation. A boundary type numerical scheme is established, and the effect of the orientation of the principle axis on the stress intensity factor is studied. The interaction between two coplanar square cracks are also modeled and discussed.

Shrink Fit of a Thick-Walled Cylinder With Contact Shear

1968 ◽  
Vol 35 (4) ◽  
pp. 729-736 ◽  
Author(s):  
L. R. Hill ◽  
A. S. Cakmak ◽  
R. Mark
Keyword(s):  
Coefficient Of Thermal Expansion ◽  
Mixed Boundary ◽  
Three Dimensional ◽  
Displacement Fields ◽  
Dual Integral Equations ◽  
Two Phase ◽  
Stress And Displacement Fields ◽  
Shrink Fit ◽  
Finite Band ◽  
Shear Condition

The shrink fit of a finite band on an infinite elastic thick-walled circular cylinder is formulated in terms of inhomogeneous dual integral equations. The solution is obtained by the series method for the case of a prescribed uniform radial displacement and an arbitrary contact shear. A three dimensional photoelastic experiment was performed to provide a realistic contact shear condition and to confirm the analytical solution. The model loading fixture was based on the high coefficient of thermal expansion and the two-phase character of epoxy. The resulting stress and displacement fields are compared with those of a similar mixed boundary value problem neglecting the contact shear.

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