Stress Concentrations and Static Failure for Common Elements used in Finite Element Stress Analysis

Element types that are commonly used in practice for a static finite element stress analysis include the truss element, beam element, plane stress/strain elements, axisymmetric elements, and solid elements.This paper focuses on stress concentrations and static failure associated with these elements and serves as a reference for instructors and practitioners.Stress concentrations and static failure for these elements has not been comprehensively addressed in any finite element textbook.The first author has integrated stress concentrations and static failure into introductory finite element undergraduate courses, graduate courses and industrial short courses.The authors have found through experience that students and practitioners are not familiar with the stress concentrations and static failure associated with these elements. Proceedings of the 2007 Midwest Section Conference of the American Society for Engineering EducationAn understanding of the failure modes associated with each component in a structure is required to ensure that it will not fail under loading.Static failure modes for different components can be readily found in mechanics of materials and machine design textbooks.The most common static failure criteria found in finite element textbooks is the von Mises applied to plane stress/strain elements, axisymmetric elements, and solid elements.A review of finite element textbooks reveals that there is no discussion on why the von Mises criterion was selected and other failure criterion are not considered.The authors are not aware of any finite element textbook that address the static failure modes associated with beam element and there is very limited discussion for the truss element.The goal of this paper is to define the stress concentrations and static failure for finite elements commonly used to carry out a static, linear elastic, stress analysis.The elements considered include the truss element, beam element, plane stress/strain elements, axisymmetric elements, and solid elements as shown in Figure 1.Each element will be considered separately in this paper and the following will be discussed: overview that includes a literature review, stress concentrations, and static failure.This paper will serve as a reference for instructors and practitioners.