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Others say " in ductile materials the local stress concentrations can be ignored, and then it is permissible for the stress to exceed the material yield stress". People use the phrase "singularity, you can forget it", but is very important to put attention to peak stresses, not simply forgeting, very dangerous!!.
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RE: How to explain this singularity? rb1957 (Aerospace) 14 Feb 22 15:26 mathematical model of real structure) which mathematically produces infinite or higher stress values. Discretization/meshing introduces singular points in our FEA model (which is nothing but approx. Some finite radius will always be present at corner and finite area resist the stresses at corner and hence the stress will be finite in real structures. In reality, we cannot make perfect corner or anything that is perfectly round, square, flat etc. At the sharp corner, the resistance to the stress is concentrated at a corner point and hence the stress values are higher than adjoining area.
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(Its different from stress at point to find out stress tensor components.) As the area approaches zero (consider point as nearly zero area) stress values tend to infinity. Similarly, now consider the values of stress at point. The value of f(x) at x=0 is infinity or cannot be defined and the function is called singular at x=0. The singularity of mathematical function is point at which the function's value can not be defined or in other words value approaches infinity. First let us consider singularity in mathematics.