In the 2D laminate transformation, what are m and n defined as?

In the 2D laminate transformation, what are m and n defined as?

• A. m = cos theta, n = sin theta
• B. m = sin theta, n = cos theta
• C. m = tan theta, n = sec theta
• D. m = theta, n = pi/2

Answer: (A)

In 2D laminate transformation, m and n are the direction cosines of the rotated x' axis with respect to the original x and y axes. For a ply rotated by angle theta, the unit vector along x' has components (cos theta, sin theta) in the original coordinate system. Therefore m = cos theta and n = sin theta. These values are used in the transformation of stresses and stiffness, producing terms like m^2, n^2, and 2mn that correspond to cos^2 theta, sin^2 theta, and sin theta cos theta, ensuring the rotation is represented correctly. The other options would not form the proper unit-direction components of the rotated axis.

In 2D laminate transformation, m and n are the direction cosines of the rotated x' axis with respect to the original x and y axes. For a ply rotated by angle theta, the unit vector along x' has components (cos theta, sin theta) in the original coordinate system. Therefore m = cos theta and n = sin theta. These values are used in the transformation of stresses and stiffness, producing terms like m^2, n^2, and 2mn that correspond to cos^2 theta, sin^2 theta, and sin theta cos theta, ensuring the rotation is represented correctly. The other options would not form the proper unit-direction components of the rotated axis.