Structural stability and failure analysis using peridynamic theory

Abstract The peridynamic theory has been successfully utilized for damage prediction in many problems. However, the elastic stability of structures has not been studied using the peridynamic theory. Therefore, this paper investigates the elastic stability of simple structures to determine buckling characteristics of the peridynamic theory by considering two sets of problems. The first set of problems involves rectangular columns under compression to find the effects of the cross-sectional area and boundary conditions on buckling load. The second set involves rectangular plates under a uniform temperature load to establish the effects of plate dimensions and material properties on the critical buckling temperature. The predictions of the peridynamic theory agree with those published in the literature. The solution method is based on reducing the peridynamic equations of motion to discrete forms by using collocation points. These discrete equations are then solved using adaptive dynamic relaxation. Furthermore, perturbation method using geometrical imperfections is utilized to trigger lateral displacements in the numerical solutions.

[1]  S. Silling,et al.  Peridynamic modeling of membranes and fibers , 2004 .

[2]  Dominik Rogula,et al.  Nonlocal theory of material media , 1982 .

[3]  Shahid H. Bokhari,et al.  A Partitioning Strategy for Nonuniform Problems on Multiprocessors , 1987, IEEE Transactions on Computers.

[4]  A. Cemal Eringen,et al.  On the Problem of Crack Tip in Nonlocal Elasticity , 1974 .

[5]  Jifeng Xu,et al.  Peridynamic analysis of damage and failure in composites. , 2006 .

[6]  Richard H. Gallagher,et al.  Perturbation procedures in nonlinear finite element structural analysis , 1975 .

[7]  S. Silling.  Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces , 2000 .

[8]  E. Kröner,et al.  Elasticity theory of materials with long range cohesive forces , 1967 .

[9]  A. Cemal Eringen,et al.  Stress concentration at the tip of crack , 1974 .

[10]  I. Kunin,et al.  Elastic Media with Microstructure I: One-Dimensional Models , 1982 .

[11]  S. Timoshenko.  Theory of Elastic Stability , 1936 .

[12]  Erdogan Madenci,et al.  Effect of void content on stiffness and strength of composites by a peridynamic analysis and static indentation test , 2007 .

[13]  Jifeng Xu,et al.  Damage and Failure Analysis of Composite Laminates Under Biaxial Loads. , 2007 .

[14]  E. Dill,et al.  An Introduction to the Mechanics of Solids , 1972 .

[15]  Bahattin Kilic,et al.  Peridynamic theory for progressive failure prediction in homogeneous and heterogeneous materials , 2008 .

[16]  Stewart Andrew Silling,et al.  Dynamic fracture modeling with a meshfree peridynamic code , 2003 .

[17]  A. Eringen,et al.  On nonlocal elasticity , 1972 .

[18]  Stewart Andrew Silling,et al.  Peridynamic Modeling of Impact Damage , 2004 .

[19]  W. T. Koiter,et al.  ELASTIC STABILITY AND POST-BUCKLING BEHAVIOUR , 2001 .

[20]  S. Silling,et al.  A meshfree method based on the peridynamic model of solid mechanics , 2005 .

[21]  Nicolas Sau,et al.  Peridynamic modeling of concrete structures , 2007 .