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A mixed DOF collocation method for elastic problems in heterogeneous structure
Author(s) -
Yang Mao,
Lu Shan
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6087
Subject(s) - discretization , discontinuity (linguistics) , collocation (remote sensing) , stiffness matrix , stiffness , mathematics , collocation method , matrix (chemical analysis) , convergence (economics) , boundary (topology) , direct stiffness method , mathematical analysis , boundary value problem , geometry , computer science , structural engineering , differential equation , materials science , ordinary differential equation , engineering , machine learning , economic growth , economics , composite material
Summary In this paper, a collocation method with mixed degrees of freedom (DOFs) is proposed for heterogeneous structures. Local tractions of the outer and interface boundaries are introduced as DOFs in the mixed collocation scheme. Then, the equilibrium equations of all the nodes and the outer boundary conditions are discretized and assembled into the global stiffness matrix. A local force equilibrium equation for modeling the stress discontinuity through the interface is developed and added into the global stiffness matrix as well. With those contributions, a statically determined stiffness matrix is obtained. Numerical examples show that the present method is superior to the classical mixed collocation method in the heterogeneous structure because it improves the accuracy and the convergence and remains the efficiency. Besides, almost constant convergence rates of displacements and stresses are found in all the examples, even for three‐dimensional problems.