Groove Bottom Contours of Minimum Stress Concentration for Antiplane Shear Deformation

1985 ◽  
Vol 52 (2) ◽  
pp. 379-384 ◽  
Author(s):  
B. H. Eldiwany ◽  
L. T. Wheeler
Keyword(s):  
Stress Concentration ◽  
Numerical Methods ◽  
Shear Deformation ◽  
Half Space ◽  
Optimization Problems ◽  
Integral Form ◽  
Antiplane Shear ◽  
Space Boundary ◽  
Minimum Stress ◽  
Special Case

Results from free streamline hydrodynamics are exploited in order to solve optimization problems for antiplane shear deformation, in which the stress concentration is to be minimized. These problems pertain to the optimum shapes for grooves cut into a half-space. We obtain results, which from the standpoint of the hydrodynamics problem, complement those presently in the literature. The solution is given in an integral form which in general must be evaluated by numerical methods, but that reduces to elliptic integrals for the special case of a notch whose faces meet the half-space boundary at right angles.

Nonlinear oscillations in a constant gravitational field

2021 ◽  
Author(s):  
Stylianos - Vasileios Kontomaris ◽  
Anna Malamou
Keyword(s):  
Gravitational Field ◽  
Numerical Methods ◽  
Differential Equations ◽  
Half Space ◽  
Nonlinear Oscillations ◽  
Elastic Half Space ◽  
Rigid Sphere ◽  
Elementary Functions ◽  
Approximate Expressions ◽  
Special Case

Abstract Exploring non-linear oscillations is a challenging task since the related differential equations cannot be directly solved in terms of elementary functions. Thus, complicated mathematical or numerical methods are usually employed to find accurate or approximate expressions that describe the behavior of the system with respect to time. In this paper, the vertical oscillations of an object under the influence of its weight and an opposite force with magnitude F=cyn, where n>0 are being explored. Accurate and approximate simple solutions regarding the object’s position with respect to time are presented and the dependence of the oscillation’s period from the oscillation’s range of displacements and the exponent n is revealed. In addition, the special case in which n=3/2 (which describes the oscillation of a rigid sphere on an elastic half space) is also highlighted. Lastly, it is shown that similar cases (such as the case of a force with magnitude F=kx+λx2) can be also treated using the same approach.

Effect of Stress Concentration on Laminated Plates

2012 ◽  
Vol 29 (2) ◽  
pp. 241-252 ◽  
Author(s):  
A. S. Sayyad ◽  
Y. M. Ghugal
Keyword(s):  
Stress Concentration ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Shear Stresses ◽  
Normal Strain ◽  
Concentrated Load ◽  
Transverse Shear Stresses

AbstractThis paper deals with the problem of stress distribution in orthotropic and laminated plates subjected to central concentrated load. An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is used to obtain in-plane normal and transverse shear stresses through the thickness of plate. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. A simply supported plate with central concentrated load is considered for the numerical analysis. Anomalous behavior of inplane normal and transverse shear stresses is observed due to effect of stress concentration compared to classical plate theory and first order shear deformation theory.

Parameter Sensitivity Analysis of a Large-Scale System With Several Components Interacting in Series

1989 ◽  
Author(s):  
H. Torab
Keyword(s):  
Sensitivity Analysis ◽  
Large Scale ◽  
Optimization Problems ◽  
Parameter Sensitivity ◽  
Engineering Optimization ◽  
Parameter Sensitivity Analysis ◽  
Large Scale Systems ◽  
In Series ◽  
Special Case ◽  
Engineering Optimization Problems

Abstract Parameter sensitivity for large-scale systems that include several components which interface in series is presented. Large-scale systems can be divided into components or sub-systems to avoid excessive calculations in determining their optimum design. Model Coordination Method of Decomposition (MCMD) is one of the most commonly used methods to solve large-scale engineering optimization problems. In the Model Coordination Method of Decomposition, the vector of coordinating variables can be partitioned into two sub-vectors for systems with several components interacting in series. The first sub-vector consists of those variables that are common among all or most of the elements. The other sub-vector consists of those variables that are common between only two components that are in series. This study focuses on a parameter sensitivity analysis for this special case using MCMD.

Efficient Numerical Solution of Inverse Heat Conduction Problems

1995 ◽  
Author(s):  
Hans-Jürgen Reinhardt ◽  
Dinh Nho Hao
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Numerical Methods ◽  
Stationary Point ◽  
Forthcoming Paper ◽  
Inverse Heat Conduction ◽  
Piecewise Constant ◽  
Numerical Tests ◽  
Inverse Heat Conduction Problems ◽  
Special Case

Abstract In this contribution we propose new numerical methods for solving inverse heat conduction problems. The methods are constructed by considering the desired heat flux at the boundary as piecewise constant (in time) and then deriving an explicit expression for the solution of the equation for a stationary point of the minimizing functional. In a very special case the well-known Beck method is obtained. For the time being, numerical tests could not be included in this contribution but will be presented in a forthcoming paper.

SH pulse in an elastic wedge

1973 ◽  
Vol 63 (5) ◽  
pp. 1571-1582
Author(s):  
A. M. Abo-Zena ◽  
Chi-Yu King
Keyword(s):  
Integral Transform ◽  
Wedge Angle ◽  
Integral Form ◽  
Diffraction Effect ◽  
Elastic Wedge ◽  
Sh Waves ◽  
Wedge Surface ◽  
Line Parallel ◽  
Finite Set ◽  
Special Case

abstract This paper gives an analysis of the response of an elastic wedge of arbitrary angle to an impulsive SH source applied on the wedge surface along a line parallel to the edge of the wedge. A two-dimensional time-dependent Green's function for SH waves is constructed from an integral-transform approach. The result is given in a closed form for the incident and the reflected pulses and in an integral form for the diffracted pulse from the edge. For the special case that the wedge angle is an integral fraction of π, the result is interpretable in terms of a finite set of image sources with no diffraction effect. Numerical examples are given for illustration.

scholarly journals Engineering Design Driven by Models and Measures: The Case of a Rigid Inflatable Boat

2018 ◽  
Author(s):  
Cristiano Fragassa
Keyword(s):  
Numerical Methods ◽  
Engineering Design ◽  
Design Process ◽  
Experimental Approach ◽  
Numerical Models ◽  
Stress And Strain ◽  
Engineering Design Process ◽  
Hull Slamming ◽  
Available Information ◽  
Special Case

Rigid-hulled inflatable boats are extremely practical and popular nowadays. They offer a effective conciliation among usability and costs. Their stable and seaworthy behaviour is guaranteed by performing hydroplaning hulls coupled with unsinkable inflated tubes. At the same time, their design is often based on tradition and preconceptions. Rarely, the design assumptions are validated by the reality or, even, by deeper investigations. In this article, both numerical methods and experimental mechanics techniques are proposed as an essential way for supporting the designers in their decisive tasks. Three different situations are detailed where a numerical or an experimental approach shows its benefit inside the engineering design process: firstly permitting to investigate the behaviour of materials driving the fiberglass selection; then measuring the levels of stress and strain in the hull during sailing; finally, using all available information as a base for developing numerical models of the hull slamming in waves. Even if the discussion is focused on a rigid inflatable boat, large part of its considerations is relevant beyond this special case.

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