Studies in collapse analysis of rigid-plastic plates with a square yield diagram

1957 ◽  
Vol 241 (1226) ◽  
pp. 311-338 ◽  
Keyword(s):  
Reinforced Concrete ◽  
Boundary Conditions ◽  
Upper Bound ◽  
Plastic Plate ◽  
Rigid Plastic ◽  
Concentrated Load ◽  
Arbitrary Boundary ◽  
Loaded Plate ◽  
Concrete Plate ◽  
Collapse Analysis

The collapse loads and mechanisms of a rigid-plastic plate with a square yield diagram, such as continuously reinforced concrete plate, are considered. Particular attention is paid to the case of a single concentrated load applied to a plate of arbitrary plan and with arbitrary boundary conditions. Upper-bound solutions are also given for a uniformly loaded plate of regular polygonal plan.

scholarly journals Rigid plastic plates at large deformations

1985 ◽  
Vol 7 (1) ◽  
pp. 20-23
Author(s):  
Vu Van The
Keyword(s):  
Reinforced Concrete ◽  
Boundary Conditions ◽  
Large Deformations ◽  
Plate Thickness ◽  
Large Deflections ◽  
Rigid Plastic ◽  
Collapse Pressure ◽  
Yield Load ◽  
Yield Behaviour ◽  
Relationship Of

By being statically loaded plastic plates can support loads exceeding the bending collapse pressure, the behaviour of perfectly rigid plastic plates beyond the yield load depends on changes in geometry to the plastic flow. Therefore in post yield behaviour the deflection can not be considered small in comparison with the plate thickness. In this paper we employ the equations of plates at moderately large deflections and the approximate live behaviour of plates introduced in/2,3/ by dividing plates into a number of rigid regions which have been separated by line hinges situated at locations where their discontinue ties in w,i occur, an estimative method of the toad - deflection relationship of arbitrarily shaped plates having arbitrarily boundary conditions is developed. This method is directly extended to anisotropic and reinforced concrete plates.

A Variational Upper-Bound Method for Plane Strain Problems

1996 ◽  
Vol 118 (3) ◽  
pp. 301-309 ◽  
Author(s):  
Wei-Ching Yeh ◽  
Yeon-Sheng Yang
Keyword(s):  
Boundary Conditions ◽  
Upper Bound ◽  
Metal Flow ◽  
Variational Calculus ◽  
Experimental Result ◽  
Natural Boundary ◽  
Rigid Plastic ◽  
Upper Bound Method ◽  
Natural Boundary Conditions

In this paper, a variational upper-bound (VUB) method is proposed. It is the method that determines an upper-bound solution using variational calculus. By using the method, a set of so called “naturally boundary conditions,” which were all ignored in past investigations, can be theoretically derived for the rigid/plastic interface assumed to be arbitrary function in prior. This method is shown to be applicable to the cup ironing problem. From the result we can clearly indicate the role of these natural boundary conditions which reasonably account for the effect of friction on the pattern of metal flow. The VUB method not only presents an improvement on the traditional upper-bound method, but also favorably agrees with experimental result of Nielsen et al. (1963) in calculating upper-bound energy.

Experimental Study and Numerical Simulation for Explosion and Phenomena of RC Slabs

2014 ◽  
Vol 501-504 ◽  
pp. 1096-1103
Author(s):  
Hong Xiao Wu ◽  
Hao Zhe Xing ◽  
Zhi Fang Yan
Keyword(s):  
Reinforced Concrete ◽  
Impact Loading ◽  
Loading Condition ◽  
Damage Mechanism ◽  
Failure Characteristics ◽  
Explosion Pressure ◽  
Concrete Plate ◽  
Solid Models ◽  
Calculation Results ◽  
Rc Slabs

The blast impact dynamic experiment of reinforced concrete rectangular plate with simply supported boundary conditions was performed using explosion pressure simulator. With 3-D FEM software LS-DYNA, the separate solid models of concrete and steel were established and 3-D FEM dynamic analysis of the experiment process was carried out. Compared calculation results to experiment results synthetically, the damage mechanism and failure characteristics of reinforced concrete plate under explosion impact loading condition were got and it is also verified that the H-J-C model can approximately simulate the concrete properties well under explosion impact loading condition.

scholarly journals A Unified Spectro-Geometric-Ritz Method for Vibration Analysis of Open and Closed Shells with Arbitrary Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-30 ◽  
Author(s):  
Dongyan Shi ◽  
Yunke Zhao ◽  
Qingshan Wang ◽  
Xiaoyan Teng ◽  
Fuzhen Pang
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Analysis Model ◽  
Arbitrary Boundary ◽  
Fourier Cosine ◽  
Auxiliary Functions ◽  
Arbitrary Boundary Conditions ◽  
Closed Shells

This paper presents free vibration analysis of open and closed shells with arbitrary boundary conditions using a spectro-geometric-Ritz method. In this method, regardless of the boundary conditions, each of the displacement components of open and closed shells is represented simultaneously as a standard Fourier cosine series and several auxiliary functions. The auxiliary functions are introduced to accelerate the convergence of the series expansion and eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries. The boundary conditions are modeled using the spring stiffness technique. All the expansion coefficients are treated equally and independently as the generalized coordinates and determined using Rayleigh-Ritz method. By using this method, a unified vibration analysis model for the open and closed shells with arbitrary boundary conditions can be established without the need of changing either the equations of motion or the expression of the displacement components. The reliability and accuracy of the proposed method are validated with the FEM results and those from the literature.

Free vibration analysis of three-layer thin cylindrical shell with variable thickness two-dimensional FGM middle layer under arbitrary boundary conditions

2021 ◽  
pp. 109963622110204
Author(s):  
Xue-Yang Miao ◽  
Chao-Feng Li ◽  
Yu-Lin Jiang ◽  
Zi-Xuan Zhang
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Volume Fraction ◽  
Ritz Method ◽  
Admissible Function ◽  
Free Vibration Analysis ◽  
Middle Layer ◽  
Two Dimensional ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions

In this paper, a unified method is developed to analyze free vibrations of the three-layer functionally graded cylindrical shell with non-uniform thickness. The middle layer is composed of two-dimensional functionally gradient materials (2D-FGMs), whose thickness is set as a function of smooth continuity. Four sets of artificial springs are assigned at the ends of the shells to satisfy the arbitrary boundary conditions. The Sanders’ shell theory is used to obtain the strain and curvature-displacement relations. Furthermore, the Chebyshev polynomials are selected as the admissible function to improve computational efficiency, and the equation of motion is derived by the Rayleigh–Ritz method. The effects of spring stiffness, volume fraction indexes, configuration on of shell, and the change in thickness of the middle layer on the modal characteristics of the new structural shell are also analyzed.

scholarly journals Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Huimin Liu ◽  
Fanming Liu ◽  
Xin Jing ◽  
Zhenpeng Wang ◽  
Linlin Xia
Keyword(s):  
Boundary Conditions ◽  
Admissible Function ◽  
Three Dimensional ◽  
Future Research ◽  
Pasternak Foundation ◽  
Arbitrary Boundary ◽  
Thick Plates ◽  
Arbitrary Boundary Conditions ◽  
Ritz Procedure ◽  
Three Dimensional Elasticity

This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique.

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