RECONSTRUCTION OF THE TIME DEPENDENCE OF A TRANSIENT BOUNDARY LOAD APPLIED TO A THREE-DIMENSIONAL ISOTROPIC LINEARLY ELASTIC SOLID

2021 ◽  
Vol 56 (6) ◽  
pp. 1004-1012
Author(s):  
I.P. Markov ◽  
L.A. Igumnov
Keyword(s):  
Time Dependence ◽  
Three Dimensional ◽  
Elastic Solid ◽  
Boundary Load

Crystallization Time Dependence of Nanohybrid Shish-Kebab Structure in HDPE/PA66 Nanofibers Composites via Solution Crystallization

2011 ◽  
Vol 110-116 ◽  
pp. 3786-3790
Author(s):  
Wen Juan Han ◽  
Guo Qiang Zheng ◽  
Yan Yan Liang ◽  
Chun Tai Liu ◽  
Chang Yu Shen
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Time Dependence ◽  
Isothermal Crystallization ◽  
Three Dimensional ◽  
Crystallization Time ◽  
Two Dimensional ◽  
Solution Crystallization ◽  
Dimensional Growth ◽  
Scanning Electron

In this study, PA66 nanofibers were successfully solution electrospun. The crystalline morphological features of HDPE solution induced by nanofibers were investigated by scanning electron microscopy (SEM). Nanohybrid shish-kebab (NHSK) can be formed in HDPE solution via isothermal crystallization, in which PA66 nanofibers serve as shish and HDPE lamellae act as kebabs surrounding the nanofibers periodically. Additionally, crystallization time has significant effect on the structure of HDPE kebab in NHSK, i.e., as crystallization time increases, the size of the kebab increases and the crystals decorated on PA66 nanofibers exhibit a three-dimensional growth (i.e., aggregate of crystallites) rather than a two-dimensional one (i.e., disc-like lamellae normal to the axis of nanofiber).

Lamb’s problem: a brief history

2019 ◽  
Vol 25 (3) ◽  
pp. 501-514
Author(s):  
Mohamad Emami ◽  
Morteza Eskandari-Ghadi
Keyword(s):  
Special Interest ◽  
Mathematical Theory ◽  
Three Dimensional ◽  
Elastic Solid ◽  
Theory Of Elasticity ◽  
Scientific Investigation ◽  
Lamb’S Problem ◽  
Solution Methods ◽  
Dimensional Version ◽  
History Of

In this review note, a historical scientific investigation is presented for Lamb’s problem in the mathematical theory of elasticity. This problem first appeared in 1904 in the pioneering paper of Professor Sir Horace Lamb (Lamb, H. On the propagation of tremors over the surface of an elastic solid. Philos Trans R Soc Lon 1904; 203: 1–42). Of special interest here are the analytical studies of the three-dimensional version of Lamb’s problem, which consists of a semi-infinite, homogeneous, isotropic elastic solid that is set in motion by the exertion of a dynamical point force applied suddenly on the surface of the domain. The objective of this paper is to offer a comprehensive introduction to Lamb’s problem for the reader, along with discussing its mathematical complexities. An account is given of the history of this ever-significant problem from its earlier stages to the more recent investigations via outlining and discussing different rigorous approaches and methods of solution that have been hitherto suggested. The limitations of different methods, if they exist, are also discussed. Eventually, various solution methods are compared considering their nature, advantages, and restrictions.

scholarly journals New Analytical Model Used in Finite Element Analysis of Solids Mechanics

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1401 ◽  
Author(s):  
Sorin Vlase ◽  
Adrian Eracle Nicolescu ◽  
Marin Marin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Elastic Solid ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Element Analysis ◽  
Elastic Multibody System

In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a system of first-order equations. However, this can also be achieved directly and naturally if Hamilton’s equations are used. The paper presents this useful alternative formalism used in conjunction with the finite element method for MBSs. The motion equations in the very general case of a three-dimensional motion of an elastic solid are obtained. To illustrate the method, two examples are presented. A comparison between the integration times in the two cases presents another possible advantage of applying this method.

Separable K-Canonical Formulation of Rectangular Element and Symplectic Integration Method for Analysis of Laminated Plates

2011 ◽  
Vol 194-196 ◽  
pp. 1496-1505
Author(s):  
Guang Hui Qing ◽  
Liang Wang ◽  
Li Zhong Shi
Keyword(s):  
Three Dimensional ◽  
Elastic Solid ◽  
Canonical System ◽  
Laminated Plates ◽  
Linear Elastic ◽  
Canonical Formulation ◽  
Single Plate ◽  
Static Responses ◽  
Rectangular Element ◽  
Symplectic Schemes

In the state space framework, a separable K-canonical formulation of rectangular element and explicit symplectic schemes for the static responses analysis of three-dimensional (3D) laminated plates are proposed in this paper. Firstly, the modified Hellinger-Reissner (H-R) variational principle for linear elastic solid is simply mentioned. Secondly, the separable J-canonical system with Hamiltonian H and the separable K-canonical formulation of rectangular element are constructed. Thirdly, on the basis of the symplectic difference schemes, the explicit symplectic schemes are employed to solve the separable K-canonical governing equation for a single plate. Then, to obtain the high accurate numerical results, a multi-scale iterative technique is also presented. Finally, based on the interlaminar compatibility condition (displacements and stresses), the excellent performance of the method presented in this paper is demonstrated by several numerical experiments of the static responses of laminated plates.

Eigenfunctions at a Singular Point in Transversely Isotropic Materials Under Axisymmetric Deformations

1985 ◽  
Vol 52 (3) ◽  
pp. 565-570 ◽  
Author(s):  
T. C. T. Ting ◽  
Yijian Jin ◽  
S. C. Chou
Keyword(s):  
Asymptotic Solution ◽  
Three Dimensional ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Axisymmetric Deformation ◽  
The Body ◽  
Isotropic Materials ◽  
Plane Strain Deformation ◽  
Polar Coordinate ◽  
Transversely Isotropic Materials

When a two-dimensional elastic body that contains a notch or a crack is under a plane stress or plane strain deformation, the asymptotic solution of the stress near the apex of the notch or crack is simply a series of eigenfunctions of the form ρδf (ψ,δ) in which (ρ,ψ) is the polar coordinate with origin at the apex and δ is the eigenvalue. If the body is a three-dimensional elastic solid that contains axisymmetric notches or cracks and subjected to an axisymmetric deformation, the eigenfunctions associated with an eigenvalue contains not only the ρδ term, but also the ρδ+1, ρδ+2… terms. Therefore, the second and higher-order terms of the asymptotic solution are not simply the second and subsequent eigenfunctions. We present the eigenfunctions for transversely isotropic materials under an axisymmetric deformation. The degenerate case in which the eigenvalues p1 and p2 of the elasticity constants are identical is also considered. The latter includes the isotropic material as a special case.

A Survey of Macro-Microcrack Interaction Problems

2000 ◽  
Vol 53 (5) ◽  
pp. 117-146 ◽  
Author(s):  
Vera Petrova ◽  
Vitauts Tamuzs ◽  
Natalia Romalis
Keyword(s):  
Three Dimensional ◽  
Elastic Solid ◽  
Singular Integral Equations ◽  
Crack Location ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Microcrack Interaction ◽  
The Impact ◽  
The Continuum ◽  
Model Approach

The results obtained on the problem of the interaction between a large crack and an array of microcracks or other microdefects are reviewed. The following problems are considered: interaction of main crack with microcracks in the two-dimensional case at tensile, shear or combined stress state; a closure of macro or microcracks as a result of their interaction, and the influence of this phenomenon on the stress intensity factor; the thermal cracking of an elastic solid caused by the macro-microcracks interaction and cracks closure; the interaction of a crack with an array of small pores or rigid inclusions; three-dimensional problems of the interaction of a penny-shaped crack with small penny-shaped microcracks. Discussed analytical results are based on the asymptotic analysis and the series solution to systems of singular integral equations describing the interaction of the macrocrack and microdefects. The series solutions were obtained with respect to the small parameter representing the ratio of micro- to macrocrack sizes. Throughout the review, the known solutions on the crack interaction are surveyed. The comparison with solutions to other relevant problems such as an interaction of semi-infinite crack with an array of finite cracks is given. The impact of a close crack location, and a comparison with relevant results of the continuum model approach are discussed. This review article includes 332 references.

A Numerical Solution of Three-Dimensional Problems in Dynamic Elasticity

1970 ◽  
Vol 37 (1) ◽  
pp. 116-122 ◽  
Author(s):  
W. W. Recker
Keyword(s):  
Dynamic Deformation ◽  
Three Dimensional ◽  
Elastic Solid ◽  
System Of Difference Equations ◽  
Order Accuracy ◽  
First Order ◽  
Dynamic Elasticity ◽  
Approximate Integral ◽  
Explicit Determination

The equations governing the dynamic deformation of an elastic solid are considered as a symmetric hyperbolic system of linear first-order partial-differential equations. The characteristic properties of the system are determined and a numerical method for obtaining the solution of mixed initial and boundary-value problems in elastodynamics is presented. The method, based on approximate integral relations along bicharacteristics, is an extension of the method proposed by Clifton for plane problems in dynamic elasticity and provides a system of difference equations, with second-order accuracy, for the explicit determination of the solution. Application of the method to a problem which has a known solution provides numerical evidence of the convergence and stability of the method.

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