Analysis of elastic and elastic-plastic adhesive joints using a mathematical programming approach

Abstract This paper is concerned with the stress analysis of adhesive joints. Aiming at a geometrically two-dimensional treatment of the adhesive, a linear displacement field through its thickness is assumed. Using the principle of virtual work and assuming linear elastic behaviour, equilibrium and constitutive equations are derived. In the case of a thin adhesive, these equations are simplified and the description so obtained is used also in the case of an elastic-perfectly plastic adhesive. In the case of elastic adhesive two different variational formulations are given: one in displacements and one mixed in displacements and adhesive tractions. In the elastic-plastic case a mixed formulation is given. Using these variational formulations finite element discretizations are performed. The matrix equations obtained in the elastic-plastic case are shown to be equivalent to a problem of mathematical programming: a parametric linear complementarity problem (LCP) involving derivatives. A solution algorithm previously used for contact problems with friction is proposed. As an application of the theory presented, an elastic-plastic analysis of a shear loaded adhesive joint test specimen is carried out.

[1]  Robert D. Adams,et al.  Stress analysis of adhesive-bonded lap joints , 1974 .

[2]  G. Maier.  Incremental plastic analysis in the presence of large displacements and physical instabilizing effects , 1971 .

[3]  A. Klarbring,et al.  General contact boundary conditions and the analysis of frictional systems , 1986 .

[4]  G. Bfer,et al.  An isoparametric joint/interface element for finite element analysis , 1985 .

[5]  Ikuyo Kaneko.  A parametric linear complementarity problem involving derivatives , 1978, Math. Program..

[6]  J. Comyn,et al.  Structural Adhesive Joints in Engineering , 1984, The Aeronautical Journal (1968).

[7]  William C. Carpenter.  Finite element analysis of bonded connections , 1973 .

[8]  A. Klarbring.  A mathematical programming approach to three-dimensional contact problems with friction , 1986 .

[9]  A. S . Kuo.  A Two-Dimensional Shear Spring Element , 1984 .

[10]  Giulio Maier,et al.  Combined elastoplastic and limit analysis via restricted basis linear programming , 1979 .

[11]  Carpenter,et al.  Stresses in bonded connections using finite elements , 1980 .

[12]  D. E. Grierson,et al.  Mathematical programming and nonlinear finite element analysis , 1979 .

[13]  Noboru Kikuchi,et al.  Finite element methods for constrained problems in elasticity , 1982 .

[14]  Karl-Gunnar Olsson,et al.  Hardening/Softening Plastic Analysis of Adhesive Joint , 1988 .

[15]  G. Maier.  A quadratic programming approach for certain classes of non linear structural problems , 1968 .

[16]  Richard M. Barker,et al.  Analysis of Bonded Joints in Vehicular Structures , 1973 .

[17]  H. L. Groth.  Calculation of stresses in bonded joints using the substructuring technique , 1986 .

[18]  A. Klarbring.  The Influence of Slip Hardening and Interface Compliance on Contact Stress Distributions. A Mathematical Programming Approach , 1986 .

[19]  I. U. Ojalvo,et al.  Bond Thickness Effects upon Stresses in Single-Lap Adhesive Joints , 1978 .

[20]  Ikuyo Kaneko.  Complete solutions for a class of elastic-plastic structures , 1980 .

[21]  H. Schäfer,et al.  A contribution to the solution of contact problems with the aid of bond elements , 1975 .

[22]  A. A. Cannarozzi.  On the resolution of some unilaterally constrained problems in structural engineering , 1980 .

[23]  G. Dantzig,et al.  COMPLEMENTARY PIVOT THEORY OF MATHEMATICAL PROGRAMMING , 1968 .

[24]  B. Nageswara Rao,et al.  Analysis of composite bonded joints , 1982 .