ABSTRACT
It is customary to assume that multilayered composite materials are materials made by a successive stacking of several different monolayers (also known as plies, layers, or laminae) (see Figure 8.1). In the general case each monolayer is orthotropic, distinguished by its own set of characteristics: E 1 ( k ) , E 2 ( k ) , G 12 ( k ) , v 12 ( k ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203757529/60c8358b-6811-4d21-b0be-8c0ed388508f/content/eq667.tif"/> , and h (k). Here k is the layer number in the n-layered laminate, while h (k) is the layer thickness. We will be concerned with the following coordinate systems (see Figure 8.2): the general or global coordinate system (x 1, x 2) for the multilayered composite, and the local or natural coordinate systems for the monolayers ( x 1 ( k ) , x 2 ( k ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203757529/60c8358b-6811-4d21-b0be-8c0ed388508f/content/eq668.tif"/> ). The axes of the local coordinates coincide with the monolayers’ main axes of orthotropy. If the kth monolayer is the unidirectional composite, then the x 1 ( k ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203757529/60c8358b-6811-4d21-b0be-8c0ed388508f/content/eq669.tif"/> -axis is directed along the reinforcing fibers in the material. The angle α (k) indicates the orientation of the main axes of the kth monolayer in the global coordinate system. A multilayered composite material. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203757529/60c8358b-6811-4d21-b0be-8c0ed388508f/content/fig8_1.tif"/> Monolayer natural coordinate system (<inline-formula> <alternatives> <mml:math display="inline"> <mml:mrow> <mml:msubsup> <mml:mtext>x</mml:mtext> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>k</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>,</mml:mo> <mml:msubsup> <mml:mtext>x</mml:mtext> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>k</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> <inline-graphic xlink:href="<a href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203757529/60c8358b-6811-4d21-b0be-8c0ed388508f/content/eq670.tif" target="_blank">https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203757529/60c8358b-6811-4d21-b0be-8c0ed388508f/content/eq670.tif</a>"/> </alternatives> </inline-formula>)a nd laminate global coordinate system (<italic>x</italic> <sub>1</sub>, <italic>x</italic> <sub>2</sub>). https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203757529/60c8358b-6811-4d21-b0be-8c0ed388508f/content/fig8_2.tif"/>
