The Application of the Principle of Stationary Potential Energy to Some Problems in Finite Elasticity

1965 ◽  
Vol 32 (3) ◽  
pp. 656-660 ◽  
Author(s):  
Mark Levinson
Keyword(s):  
Potential Energy ◽  
Finite Strain ◽  
Finite Elasticity ◽  
Energy Methods ◽  
Stationary Potential ◽  
Major Purpose ◽  
Energy Principle ◽  
Finite Strain Theory ◽  
Rubberlike Material ◽  
The Subject

Two applications of the principle of stationary potential energy to the finite straining of a neo-Hookean (rubberlike) material are given in this paper. The major purpose of the work presented is to illustrate the suitability of energy methods for the solution of problems in finite strain theory since the literature of the subject does not contain mention of such solutions. One problem not amenable to the usual inverse methods of finite elasticity is studied approximately. The other problem, involving a stability question of an unusual sort, is handled with ease by means of the energy principle.

Topics in Finite Elasticity: Hyperelasticity of Rubber, Elastomers, and Biological Tissues—With Examples

1987 ◽  
Vol 40 (12) ◽  
pp. 1699-1734 ◽  
Author(s):  
Millard F. Beatty
Keyword(s):  
Constitutive Equations ◽  
Mechanical Energy ◽  
Finite Elasticity ◽  
Physical Nature ◽  
Decomposition Theorem ◽  
Elastic Stability ◽  
Biological Tissues ◽  
Field Equations ◽  
Energy Principle ◽  
Hyperelastic Materials

This is an introductory survey of some selected topics in finite elasticity. Virtually no previous experience with the subject is assumed. The kinematics of finite deformation is characterized by the polar decomposition theorem. Euler’s laws of balance and the local field equations of continuum mechanics are described. The general constitutive equation of hyperelasticity theory is deduced from a mechanical energy principle; and the implications of frame invariance and of material symmetry are presented. This leads to constitutive equations for compressible and incompressible, isotropic hyperelastic materials. Constitutive equations studied in experiments by Rivlin and Saunders (1951) for incompressible rubber materials and by Blatz and Ko (1962) for certain compressible elastomers are derived; and an equation characteristic of a class of biological tissues studied in primary experiments by Fung (1967) is discussed. Sample applications are presented for these materials. A balloon inflation experiment is described, and the physical nature of the inflation phenomenon is examined analytically in detail. Results for the different materials are compared. Two major problems of finite elasticity theory are discussed. Some results concerning Ericksen’s problem on controllable deformations possible in every isotropic hyperelastic material are outlined; and examples are presented in illustration of Truesdell’s problem concerning analytical restrictions imposed on constitutive equations. Universal relations valid for all compressible and incompressible, isotropic materials are discussed. Some examples of non-uniqueness, including that of a neo-Hookean cube subject to uniform loads over its faces, are described. Elastic stability criteria and their connection with uniqueness in the theory of small deformations superimposed on large deformations are introduced, and a few applications are mentioned. Some previously unpublished results are presented throughout.

scholarly journals PENERAPAN METODE DIRECTED READING ACTIVITY (DRA) DALAM MENINGKATKAN KEMAMPUAN BERPIKIR KRITIS MAHASISWA PADA MATAKULIAH KOMUNIKASI PEMERINTAHAN DI PRODI ILMU PEMERINTAHAN UIN STS JAMBI

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Suryawahyuni Latief ◽  
YULFI ALFIKRI NOER
Keyword(s):  
Critical Thinking ◽  
Action Research ◽  
Undergraduate Students ◽  
Undergraduate Student ◽  
Major Purpose ◽  
Government Communication ◽  
Text Reading ◽  
The Subject ◽  
Two Stages ◽  
Reading Activity

The major purpose of this study is to improve the critical thinking of undergraduate student in a government communication field, UIN STS Jambi. The subject of this study was undergraduate students in semester VA in academic 2018/2019. The instruments used in this study was the last report of student results, observation paper, and a text reading with a title "hoax, de vide et impera millenial" with three questions: Q1 What does the topic about?, Q2 How do you manage the phenomenon? And Q3 How do you think about the text’s contents?. This study employs action research with two stages from October to December 2018. The result indicates that DRA methods is able to improve the critical thinking of undergraduates students.

A Global Extremum Principle in Mixed Form for Equilibrium Analysis With Elastic/Stiffening Materials (a Generalized Minimum Potential Energy Principle)

1994 ◽  
Vol 61 (4) ◽  
pp. 914-918 ◽  
Author(s):  
J. E. Taylor
Keyword(s):  
Potential Energy ◽  
Problem Formulation ◽  
Extremum Problem ◽  
Equilibrium Analysis ◽  
Minimum Potential Energy ◽  
Problem Statement ◽  
Energy Principle ◽  
Potential Energy Principle ◽  
Minimum Potential ◽  
Minimum Potential Energy Principle

An extremum problem formulation is presented for the equilibrium mechanics of continuum systems made of a generalized form of elastic/stiffening material. Properties of the material are represented via a series composition of elastic/locking constituents. This construction provides a means to incorporate a general model for nonlinear composites of stiffening type into a convex problem statement for the global equilibrium analysis. The problem statement is expressed in mixed “stress and deformation” form. Narrower statements such as the classical minimum potential energy principle, and the earlier (Prager) model for elastic/locking material are imbedded within the general formulation. An extremum problem formulation in mixed form for linearly elastic structures is available as a special case as well.

scholarly journals Energy methods for curved composite beams with partial shear interaction

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
István Ecsedi ◽  
Ákos József Lengyel
Keyword(s):  
Potential Energy ◽  
Ritz Method ◽  
Composite Beams ◽  
Reciprocity Relation ◽  
Energy Methods ◽  
Numerical Examples ◽  
Interlayer Slip

AbstractThis paper presents a derivation of the Rayleigh- Betti reciprocity relation for layered curved composite beams with interlayer slip. The principle of minimum of potential energy is also formulated for two-layer curved composite beams and its applications are illustrated by numerical examples. The solution of the presented problems are obtained by the Ritz method. The applications of the Rayleigh-Betti reciprocity relation proven are illustrated by some examples.

The Variational Principles of Coupled Systems in Fatigue Problem Undergoing Large Range Damage

2016 ◽  
Vol 835 ◽  
pp. 514-520
Author(s):  
Wen Feng Tan
Keyword(s):  
Fatigue Crack ◽  
Crack Initiation ◽  
Potential Energy ◽  
Large Range ◽  
Fatigue Crack Initiation ◽  
Form Solution ◽  
Coupled Systems ◽  
Energy Principle ◽  
Potential Energy Principle ◽  
Crack Initiation Life

The coupled systems of fatigue crack initiation problem undergoing large range damage is defined. The zero different work principle, coupled potential energy principle, coupled complementary energy principle in the coupled system is established. By using of coupled potential energy principle, Closed form solution about predicting fatigue crack initiation life of three-dimensional component which leads to large range damage is derived. Compared with reference [1], the close form solution derived from this some. It is proved that the method is correct. The method adopted in this paper is definite in mechanical concept,it can be widely used in analysis of predicting fatigue crack initiation life of various component which leads to large range damage.

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