Analysis of a Plate with Critical Point of Max. and Min

Any device or object that is designed and manufactured is expected to operate as advertised over a stated length of time. If the product does not function as expected then it is considered a failure. Failure can have many reasons. Failure is usually associated with reliability - the expression of confidence that the product will deliver on its expectation. Failure also has a practical side effect which is best attributed to Taguchi :”When a product fails, you must replace it or fix it. In either case, you must track it, transport it, and apologize for it. Losses will be much greater than the costs of manufacture, and none of this expense will necessarily recoup the loss to your reputation”. Failure is serious business and designing for actual failure is impossible because of so many variables. Instead we try and ensure that the design meets the Failure Criteria. There is no unique criteria and the designer usually satisfies the failure criteria that is appropriate for the type of the product and its underlying design. Many failure criteria are based on principal stresses rather than the standard engineering stress and strain. Since we can calculate the principal stress form the value of the engineering stress and strain at every point, we examine some of the popular failure criteria. Prior to application of such criteria we should also consider the fact that if the design is stretched beyond the elastic domain then the residual strain on the structure changes the design forever. If the bridge does not return back to its original state it is likely to cause additional problems in many ways