1994TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series AOpen access

Analysis near Apex in Three-Phase Bonded Material with Arbitrary Wedge Angles under Normal Surface Loading on the Surface. 2nd Report, Distribution of Displacement in Stress Fields with Singularity of Type .GAMMA.-.LAMBDA. and log.GAMMA..

T. Inoue, Hideo KOGUCHI, Toshio Yada

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Abstract

The singularity in the stress field near the apex in three-phase bonded material with arbitrary wedge angles depends on the combinations of material properties and the bonded wedge geometry. The stress singularity is represented by the orders O(γp-1), O(log r) and O(1) for real rootsρ, and O(γε-1 cos[η logγ]) and O(γε-1 sin[η logγ]) for complex roots ρ=ε+ιη, and every stress component (σγγ, σγθ, σθθ) is denoted as the same order. However, the order in the displacement field has not yet been clarified. In this paper, the displacement distribution near the apex in a three-phase bonded structure under surface traction is discussed for different combinations of materials and wedge angles within the theory of elasticity, and is analyzed by the finite element method (FEM). Comparing theoretical results of displacement distribution with numerical ones, it is shown that the order of displacement field in theγ-direction and that of displacement field in theθ-direction differ from each other.

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The singularity in the stress field near the apex in three-phase bonded material with arbitrary wedge angles depends on the combinations of material properties and the bonded wedge geometry. The stress singularity is represented by the orders O(γp-1), O(log r) and O(1) for real rootsρ, and O(γε-1 cos[η logγ]) and O(γε-1 sin[η logγ]) for complex roots ρ=ε+ιη, and every stress component (σγγ, σγθ, σθθ) is denoted as the same order. However, the order in the displacement field has not yet been clarified. In this paper, the displacement distribution near the apex in a three-phase bonded structure under surface traction is discussed for different combinations of materials and wedge angles within the theory of elasticity, and is analyzed by the finite element method (FEM). Comparing theoretical results of displacement distribution with numerical ones, it is shown that the order of displacement field in theγ-direction and that of displacement field in theθ-direction differ from each other.

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Available abstract

The singularity in the stress field near the apex in three-phase bonded material with arbitrary wedge angles depends on the combinations of material properties and the bonded wedge geometry. The stress singularity is represented by the orders O(γp-1), O(log r) and O(1) for real rootsρ, and O(γε-1 cos[η logγ]) and O(γε-1 sin[η logγ]) for complex roots ρ=ε+ιη, and every stress component (σγγ, σγθ, σθθ) is denoted as the same order. However, the order in the displacement field has not yet been clarified. In this paper, the displacement distribution near the apex in a three-phase bonded structure under surface traction is discussed for different combinations of materials and wedge angles within the theory of elasticity, and is analyzed by the finite element method (FEM). Comparing theoretical results of displacement distribution with numerical ones, it is shown that the order of displacement field in theγ-direction and that of displacement field in theθ-direction differ from each other.

Key concepts: Displacement field, Wedge (geometry), Singularity, Stress field, Geometry, Finite element method, Displacement (psychology), Elasticity (physics)

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Analysis near Apex in Three-Phase Bonded Material with Arbitrary Wedge Angles under Normal Surface Loading on the Surface. 2nd Report, Distribution of Displacement in Stress Fields with Singularity of Type .GAMMA.-.LAMBDA. and log.GAMMA.. — Research Paper | ScholarLens