GATE AE 2008 • Q15 MCQ • 1 Mark Aerospace Structures

Aerospace Structures

Strength of Materials & Elasticity

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Question Statement:

In a 3-D orthotropic material, the number of independent elastic constants in the linear stress-strain relationship is:

Options:

  • (A) 2
  • (B) 9
  • (C) 13
  • (D) 21

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2008 Q.15)** **1. Material Symmetry Classification in Elasticity**: - **Anisotropic (General Triclinic)**: 21 independent elastic constants. - **Monoclinic (one plane of symmetry)**: 13 independent constants. - **Orthotropic (three mutually orthogonal planes of symmetry)**: **9** independent elastic constants ($E_1, E_2, E_3, G_{12}, G_{23}, G_{31}, \nu_{12}, \nu_{23}, \nu_{31}$). - **Transversely Isotropic**: 5 independent constants. - **Isotropic**: 2 independent constants ($E, \nu$ or $\lambda, G$). **2. Official Master Key**: - **Official Answer Key**: **B** (9)
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