scholarly journals Optimal Load Sharing in Bioinspired Fibrillar Adhesives: Asymptotic Solution

2020 ◽  
Vol 88 (3) ◽  
Author(s):  
Harman Khungura ◽  
Mattia Bacca
Keyword(s):  
Asymptotic Solution ◽  
Adhesive Strength ◽  
Closed Form Solution ◽  
Load Sharing ◽  
Form Solution ◽  
Asymptotic Model ◽  
Linear Elastic ◽  
Optimal Load ◽  
Improving Accuracy ◽  
Fibrillar Adhesives

Abstract We propose here an asymptotic solution defining the optimal compliance distribution for a fibrillar adhesive to obtain maximum theoretical strength. This condition corresponds to that of equal load sharing (ELS) among fibrils, i.e., all the fibrils are carrying the same load at detachment; hence, they all detach simultaneously. We model the array of fibrils as a continuum of linear elastic material that cannot laterally transmit load (analogous to a Winkler soil). Ultimately, we obtain the continuum distribution of fibril's compliance in the closed-form solution and compare it with previously obtained data for a discrete model for fibrillar adhesives. The results show improving accuracy for an incremental number of fibrils and smaller center-to-center spacing. Surprisingly, the approximation introduced by the asymptotic model shows reduced sensitivity of the adhesive strength with respect to misalignment and improved adhesive strength for large misalignment angles.

On the Numerical Solution of One-Dimensional Continuum Problems Using the Theory of a Cosserat Point

1985 ◽  
Vol 52 (2) ◽  
pp. 373-378 ◽  
Author(s):  
M. B. Rubin
Keyword(s):  
Numerical Solution ◽  
Body Force ◽  
Closed Form Solution ◽  
Form Solution ◽  
Element Approximation ◽  
One Dimensional ◽  
Linear Elastic ◽  
Elastic Bar ◽  
Cosserat Point ◽  
Nonlinear Elastic

The theory of a Cosserat point is specialized to describe the motion of a one-dimensional continuum. Attention is focused on two problems of an elastic bar. Vibration of a linear-elastic bar is considered in the first problem and static deformation of a nonlinear-elastic bar subjected to a uniform body force is considered in the second problem. A closed-form solution is derived for each problem by dividing the bar into two elements, each of which is modeled as a Cosserat point. The predictions of the two-element approximation are shown to be very accurate.

Tooth Load Sharing in High-Contact Ratio Spur Gears

1985 ◽  
Vol 107 (1) ◽  
pp. 11-16 ◽  
Author(s):  
A. H. Elkholy
Keyword(s):  
Contact Stress ◽  
Applied Load ◽  
Normal Load ◽  
Closed Form Solution ◽  
Load Sharing ◽  
Form Solution ◽  
Spur Gears ◽  
Contact Ratio ◽  
Profile Modification ◽  
The Individual

A closed-form solution is presented for calculating the load sharing among meshing teeth in high contact ratio gearing (HCRG). The procedure is based upon the assumption that the sum of the tooth deflection, profile modification and spacing error at each of two or three pairs of contacts are all equal. It is also assumed that the sum of the normal loads contributed by each of two or three pairs of contacts is equal to the maximum normal load. Once the individual loads are determined, the tooth fillet stress, contact stress may be determined from the applied load and tooth geometry. An experimental example appears to verify the method.

scholarly journals Simulating Building Motions Using Ratios of the Building's Natural Frequencies and a Timoshenko Beam Model

2015 ◽  
Vol 31 (1) ◽  
pp. 403-420 ◽  
Author(s):  
Ming Hei Cheng ◽  
Thomas H. Heaton
Keyword(s):  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mode Shapes ◽  
Elastic Behavior ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Linear Elastic ◽  
Modal Summation

A simple prismatic Timoshenko beam model with soil-structure interaction (SSI) is developed to approximate the dynamic linear elastic behavior of buildings. A closed-form solution with complete vibration modes is derived. It is demonstrated that building properties, including mode shapes, can be derived from knowledge of the natural frequencies of the first two translational modes in a particular direction and from the building dimensions. In many cases, the natural frequencies of a building's first two vibrational modes can be determined from data recorded by a single seismometer. The total building's vibration response can then be simulated by the appropriate modal summation. Preliminary analysis is performed on the Caltech Millikan Library, which has significant bending deformation because it is much stiffer in shear.

scholarly journals Static Perturbation Analysis of Inclined Shallow Elastic Cables under general 3D-loads

2016 ◽  
Vol 5 (1) ◽  
pp. 250-259 ◽  
Author(s):  
Angelo Luongo ◽  
Daniele Zulli
Keyword(s):  
Asymptotic Solution ◽  
Closed Form ◽  
Perturbation Analysis ◽  
Lower Order ◽  
Orthonormal Basis ◽  
Closed Form Solution ◽  
Form Solution ◽  
Taut String ◽  
Mechanical Interpretation ◽  
Elastic Cables

Abstract Inclined, shallow, elastic cables under static 3D loads, arbitrarily distributed, are studied. Cables having natural length both larger or smaller than the distance between the supports (i.e. suspended or taut cables, respectively), are considered. Kinematically exact equations are derived, and projected onto an orthonormal basis intrinsic to the chord. A perturbation procedure is proposed, which extrapolates the solution relevant to the taut string, up to the desired order, and leads to a closed-form solution. Lower-order solutions are consistent with the hypotheses normally adopted in technical environment. Emphasis is given to the mechanical interpretation of the cable behavior. The asymptotic solution is compared to the explicit (not in closed-form) solution of the literature.

The Frictional Contact Problem of a Rigid Stamp Sliding over a Graded Medium

2016 ◽  
Vol 681 ◽  
pp. 155-174 ◽  
Author(s):  
M.A. Guler ◽  
M. Ozturk ◽  
A. Kucuksucu
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Frictional Contact ◽  
Fourier Transforms ◽  
Closed Form Solution ◽  
Form Solution ◽  
Linear Elastic ◽  
Rigid Stamp ◽  
Sharp Edges ◽  
Parameter Coefficient

In this study, the contact problem for a graded elastic half-plane in frictional contact with a rigid stamp is considered. The plane contact problem is assumed to be linear elastic and the Poisson's ratio is assumed to be constant. Analytical formulation of the study includes Fourier transforms of the governing equations and boundary conditions. The resulting integral equation is solved numerically. Contact pressure, in-plane stress and the stress intensity factor at the sharp edges of the contact are evaluated and demonstrated for various stamp profiles. The results are compared with a closed form solution for homogeneous isotropic half-plane indented by rigid stamps. The effects of the nonhomogeneity parameter, coefficient of friction and stamp profiles on the contact and in-plane stresses are analyzed in detail.

Finite element modelling of jointed structures

1980 ◽  
Vol 7 (3) ◽  
pp. 540-546
Author(s):  
A. H. Anis ◽  
E. F. P. Burnett ◽  
G. M. McNeice
Keyword(s):  
Finite Element ◽  
Closed Form Solution ◽  
Numerical Approach ◽  
Primary Objective ◽  
Form Solution ◽  
Continuous Systems ◽  
Concrete Wall ◽  
Fem Model ◽  
Linear Elastic ◽  
Engineering Problems

Many engineering problems involve the modelling of discontinuities within continuous systems. As it is difficult and often impossible to obtain a closed form solution a numerical approach must be adopted (e.g., finite element method (FEM)). In studying the panelized problem several FEM models were found in the literature. The primary objective of this note is, therefore, to discuss and compare three FEM models for layered joint response. The specific example that is considered is the panelized concrete wall–floor joint. Joint response is compared using each FEM model at both service loads (for the essentially linear elastic situation) and overload.

A closed-form solution for composite tunnel linings in a homogeneous infinite isotropic elastic medium

2008 ◽  
Vol 45 (2) ◽  
pp. 266-287 ◽  
Author(s):  
Hany El Naggar ◽  
Sean D. Hinchberger ◽  
K. Y. Lo
Keyword(s):  
Closed Form ◽  
Elastic Medium ◽  
Closed Form Solution ◽  
Form Solution ◽  
Tunnel Lining ◽  
Linear Elastic ◽  
Isotropic Elastic Medium ◽  
Thin Walled ◽  
Walled Cylinder ◽  
Elastic Soil

This paper presents a closed-form solution for composite tunnel linings in a homogeneous infinite isotropic elastic medium. The tunnel lining is treated as an inner thin-walled shell and an outer thick-walled cylinder embedded in linear elastic soil or rock. Solutions for moment and thrust have been derived for cases involving slip and no slip at the lining–ground interface and lining–lining interface. A case involving a composite tunnel lining is studied to illustrate the usefulness of the solution.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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