GUARANTEED UPPER AND LOWER BOUNDS ON THE UNIFORM LOAD OF CONTACT PROBLEMS IN ELASTICITY

被引：2

作者：

Mihai, L. Angela ^{[1
]}

Goriely, Alain ^{[2
]}

机构：

[1] Cardiff Univ, Sch Math, Senghennydd Rd, Cardiff CF24 4AG, S Glam, Wales

[2] Univ Oxford, Math Inst, Woodstock Rd, Oxford OX2 6GG, England

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2016年 / 76卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

unilateral contact; elastic material; finite strain deformation; variational principles; dead load; cohesion; COMPLEMENTARY ENERGY; NUMERICAL-SIMULATION; FINITE; INEQUALITIES; MECHANICS;

D O I：

10.1137/15M1046563

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Two mathematical models are developed within the theoretical framework of large strain elasticity for the determination of upper and lower bounds on the total strain energy of a finitely deformed hyperelastic body in unilateral contact with a rigid surface or with an elastic substrate. The model problems take the form of two continuous optimization problems with inequality constraints, the solutions of which are used to provide an enclosure on the uniform external load acting on the body's surface away from the contact zone.

引用

页码：1558 / 1576

页数：19

共 50 条

[1] Upper and lower bounds on quantities of interest for contact problems
Wang, Li
Zhong, Hongzhi
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2017, 317 : 817 - 835
[2] UPPER AND LOWER BOUNDS IN NON-HOMOGENEOUS PROBLEMS OF ELASTICITY THEORY
STUMPF, H
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1968, 48 (08): : T166 - &
[3] Equilibrium problems with lower and upper bounds
Chadli, O
Chiang, Y
Yao, JC
APPLIED MATHEMATICS LETTERS, 2002, 15 (03) : 327 - 331
[4] A class of equilibrium problems with lower and upper bounds
Zhang Congjun
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 63 (5-7) : E2377 - E2385
[5] UPPER AND LOWER BOUNDS IN LINEAR EIGENVALUE PROBLEMS
MASUR, EF
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 23 (07): : A682 - A682
[6] On computing upper and lower bounds on the outputs of linear elasticity problems approximated by the smoothed finite element method
Xuan, Z. C.
Lassila, T.
Rozza, G.
Quarteroni, A.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2010, 83 (02) : 174 - 195
[7] GUARANTEED LOWER BOUNDS FOR EIGENVALUES
Carstensen, Carsten
Gedicke, Joscha
MATHEMATICS OF COMPUTATION, 2014, 83 (290) : 2605 - 2629
[8] Respecting Lower Bounds in Uniform Lower and Upper Bounded Facility Location Problem
Gupta, Neelima
Grover, Sapna
Dabas, Rajni
COMPUTING AND COMBINATORICS (COCOON 2021), 2021, 13025 : 463 - 475
[9] POINTWISE UPPER AND LOWER BOUNDS FOR STATIC AND GEOMETRIC FIELDQUANTITIES IN ELASTICITY THEORY
STUMPF, H
ACTA MECHANICA, 1971, 12 (3-4) : 223 - &
[10] UPPER AND LOWER BOUNDS ON SOLUTIONS OF INITIAL VALUE PROBLEMS
BREUER, S
GOTTLIEB, D
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1971, 36 (02) : 283 - &

← 1 2 3 4 5 →