Impact of a Mass on a Column

1949 ◽  
Vol 16 (4) ◽  
pp. 370-374
Author(s):  
W. H. Hoppmann
Keyword(s):  
Elastic Support ◽  
Transverse Impact ◽  
Numerical Examples ◽  
Simply Supported

Abstract In this paper a study is made of the problem of the transverse impact of a mass on a column with simply supported ends. Consideration is also given to the case in which the column has elastic support throughout its length. Formulas are obtained for the deflections and strains. Numerical examples illustrating the theory are worked out in detail.

The Analysis and Optimization of the Reliability of Laminates Based on Probabilistic and Non-Probabilistic Hybrid Model

2012 ◽  
Vol 629 ◽  
pp. 752-756 ◽  
Author(s):  
Wen Jie Peng ◽  
Xiao Xu Huang ◽  
Rui Ge
Keyword(s):  
Reliability Analysis ◽  
Hybrid Model ◽  
Reliability Index ◽  
Numerical Examples ◽  
Uncertainty Range ◽  
Probabilistic Uncertainty ◽  
Simply Supported ◽  
Uncertain Variables ◽  
Optimization Result

The reliability analysis and optimization of laminates containing probabilistic uncertain variables and non-probabilistic bounded uncertain variables is conducted in the present paper. Convex method is utilized to deal with non-probabilistic bounded uncertain variables. The reliability index and index range of a four sides simply supported laminate are optimized for numerical examples. The results indicate that considering the non-probabilistic uncertainty variables can get more conservative results, and the larger the uncertainty range of non-probabilistic bounded uncertain variables is, the more conservative optimization result is.

scholarly journals Hygrothermo-mechanical behaviour of layered composite plates

2002 ◽  
Vol 24 (3) ◽  
pp. 142-150
Author(s):  
Tran Ich Thinh
Keyword(s):  
Finite Element ◽  
Mechanical Behaviour ◽  
Composite Plates ◽  
Layered Composite ◽  
Rectangular Plates ◽  
Fe Method ◽  
Third Order ◽  
Numerical Examples ◽  
Simply Supported ◽  
Displacement Theory

In this paper, a hygrothermo-mechanical behaviour of simply supported, composite layered rectangular plates is presented. The analysis is based on use of the Finite Element (FE) method and the full third-order displacement theory. Numerical examples are presented for symmetrically in-axis (0° /90° /90° /0°) and off-axis ( 45° / - 45° / -45° / 45°) layered rectangular plates.

Apparently First Closed-Form Solution for Frequencies of Deterministically and/or Stochastically Inhomogeneous Simply Supported Beams

2000 ◽  
Vol 68 (2) ◽  
pp. 176-185 ◽  
Author(s):  
S. Candan ◽  
I. Elishakoff
Keyword(s):  
Closed Form ◽  
Infinite Number ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Numerical Examples ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Benchmark Solutions

An infinite number of closed-form solutions is reported for a deterministically or stochastically nonhomogeneous beam, for both natural frequencies and reliabilities, for specialized cases. These solutions may prove useful as benchmark solutions. Numerical examples are evaluated.

scholarly journals Approximation of a simply supported plate with obstacle

2017 ◽  
Vol 23 (3) ◽  
pp. 348-358
Author(s):  
Cornel M Murea ◽  
Dan Tiba
Keyword(s):  
Variational Inequalities ◽  
Linear Equations ◽  
Numerical Examples ◽  
Simply Supported ◽  
Fixed Domain ◽  
Rigid Obstacle ◽  
Coincidence Set

We discuss an algorithm for the solution of variational inequalities associated with simply supported plates in contact with a rigid obstacle. Our approach has a fixed domain character, uses just linear equations and approximates both the solution and the corresponding coincidence set. Numerical examples are also provided.

Transverse Impact of a Damped Plate near a Straight Edge

1995 ◽  
Vol 117 (1) ◽  
pp. 103-108 ◽  
Author(s):  
A. N. Danial ◽  
J. F. Doyle
Keyword(s):  
Finite Element ◽  
Free Edge ◽  
Flexural Wave ◽  
Viscous Damping ◽  
Finite Element Analyses ◽  
Edge Waves ◽  
Transverse Impact ◽  
Reflected Waves ◽  
Simply Supported ◽  
Flexural Wave Propagation

The effects of boundaries on flexural wave propagation in plates with viscous damping are studied through spectral and finite element analyses of incident and reflected waves. The incident wave is generated by point impact and therefore has the complication of being circularly crested. Results show excellent agreement between finite element and spectral solutions for waves—with high and low damping—reflected from simply supported, clamped and free edges. In addition, the possibility of Rayleigh-type free edge waves are investigated.

Elastic Transverse Impact on Beams

2006 ◽  
Vol 326-328 ◽  
pp. 1559-1562
Author(s):  
Dulal Goldar
Keyword(s):  
Dynamic Stress ◽  
Weight Ratio ◽  
Dynamic Strain ◽  
Stress Distributions ◽  
Transverse Impact ◽  
Low Velocity ◽  
Structural Element ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
New Findings

Present investigation were carried out to study photoelastically the stress distributions in a simply supported beam with over- hangs subjected to a low velocity central- and quarter- spanimpact loadings by light strikers keeping beam/ striker weight ratio constant (2.675), and then comparing the results so obtained with those in similar simply supported beams made of other materials subjected to central- impact loadings from an analysis of dynamic strain gauge data. Interesting new findings were obtained from the results of the present investigation and also from results reported in the literature in this respect. Introduction. In modern times dynamic stress analysis is becoming increasingly important for various engineering applications. Although significant amount of insight in these respects have been developed, the subject being rather intricate would continue to attract of more research workers in future. A beam is a common structural element, and in several applications, simply supported beams with over- hang are employed in practice. Transverse and longitudinal bridge girders and chassis of rails- and road- wagons are some of the typical applications of the same. Here, photoelastic technique was employed to determine dynamic stress distributions in a model simply supported beam with over- hang.

scholarly journals Three-dimensional modeling of the static behavior of magneto-electro-elastic multilayer plates based on an elastic support

2019 ◽  
Vol 286 ◽  
pp. 01004 ◽  
Author(s):  
M. Hamidi ◽  
S. Zaki ◽  
M. Aboussaleh
Keyword(s):  
Boundary Conditions ◽  
Mathematical Formulation ◽  
Electrical Potential ◽  
Three Dimensional ◽  
Elastic Support ◽  
Rectangular Plates ◽  
Static Behavior ◽  
Simply Supported ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling

In this communication, the state space method is used to analyze the static behavior of laminated magneto-electro-elastic rectangular plates with simply supported boundary conditions based on an elastic support. The mathematical formulation is elaborated in a general form and an arbitrary number of layers as well as the orthotropic behavior can be considered. The methodology is based on the mixed formulation, in which basic unknowns are formed by collecting displacements, stresses, electrical displacements, electrical potential, magnetic induction and magnetic potential. As special case, multilayered rectangular plate is analyzed under the surface loading with simply supported boundary conditions based on an elastic support. The procedure of calculation shows that the formulation presented here is simple and direct.

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