A square plate of room temperature has a round hole in it. The hole is filled...
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A square plate of room temperature has a round hole in it. The hole is filled with a plug of the same material and the same thickness as the square plate. The plug exactly fits the hole if it is cooled down I degrees from room temperature. After a while the plug assumes the room temperature again and is stuck in the hole. E V a - a Assume the radius of the plug a is small compared to the dimension of the plate; The thickness of both the plate and the plug is t: The elastic modulus and Poison's ratio are E and v; and the linear expansion of the material is a Use Airy stress function and: Derive an expression for the plate which relates the stress on the edge of the hole to the displacement of this edge. (So, the plug is replaced by a stress on to the edge of the hole.) - Derive an expression for the plug which relates the stress on the edge to the displacement of the edge. (So, the plate is replaced by a stress on to the edge of the plug.) Formulate the transition conditions between the plug and the plate. Calculate the stress between the plate and the plug. Calculate the stress distribution in the plug and the plate. A square plate of room temperature has a round hole in it. The hole is filled with a plug of the same material and the same thickness as the square plate. The plug exactly fits the hole if it is cooled down I degrees from room temperature. After a while the plug assumes the room temperature again and is stuck in the hole. E V a - a Assume the radius of the plug a is small compared to the dimension of the plate; The thickness of both the plate and the plug is t: The elastic modulus and Poison's ratio are E and v; and the linear expansion of the material is a Use Airy stress function and: Derive an expression for the plate which relates the stress on the edge of the hole to the displacement of this edge. (So, the plug is replaced by a stress on to the edge of the hole.) - Derive an expression for the plug which relates the stress on the edge to the displacement of the edge. (So, the plate is replaced by a stress on to the edge of the plug.) Formulate the transition conditions between the plug and the plate. Calculate the stress between the plate and the plug. Calculate the stress distribution in the plug and the plate.
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Solving this problem involves using the theory of elasticity and the Airy stress function the steps ... View the full answer
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