Showing papers on "von Mises yield criterion published in 1969"

Elasto-plastic solutions of engineering problems ‘initial stress’, finite element approach

Abstract: The paper presents first a general formulation of the elasto-plastic matrix for evaluating stress increments from those of stresses for any yield surface with an associated flow rule. A new ‘initial stress’ computational process is proposed which is shown (1) to yield more rapid convergence than alternative approaches (2) to permit large load increments without violating the yield criteria and thus simply to establish lower bound solutions. Several solutions showing stress distribution, strain development and growth of plastic enclaves are given both for the von Mises and for Coulomb (Drucker) type yield surfaces. Load reversal and thermoplastic behaviour are dealt with.

Finite element analysis of inelastic structures.

Abstract: Differential stress-strain relationships are used to generate a system of simultaneous firstorder differential force-displacement equations which are integrated numerically to obtain the stresses, strains, and displacements in inelastic structures. For the biaxially stressed element, the concept of isotropic hardening and a generalized stress are used to evaluate an effective modulus and Poisson's ratio, which vary continuously from their initial values during elastic straining action to their asymptotic values during intense plastic straining action. The surface of plasticity for this element closely approximates the von Mises surface when the generalized stress is set equal to the von Mises stress and the strain distribution is essentially identical to that obtained by the Prandtl-Reuss incremental flow theory. The analysis of the MIT shear lag structure is presented to demonstrate the applicability of the method to systems of practical size and interest. Nomenclature A = equilibrium matrix B = compatibility matrix C = stress-strain matrix C = differential stress matrix E = Young's modulus Et = tangent modulus Es = secant modulus K — stiffness matrix K = differential stiffness matrix P = applied load parameter u = element nodal displacements X = element nodal forces X = load constant n = Poisson's ratio fjLt = tangent Poisson's. ratio Us = secant Poisson's ratio e = strain a- = normal stress

Maximum Strength Elastic Structural Design

Abstract: An energy formulation is presented for the problem of optimal design of one and two-dimensional elastic sandwich structures. The object in design is to determine the distribution of material associated with the stiffest/strongest structure. The limit on local material strength is expressed through a prescribed upper bound on the unit strain energy, when the stiffest structure has the maximum load-carrying capacity among equal volume structures of similar style. Analytical solutions are obtained for the optimal simply-supported and clamped circular sandwich plates. The counterpart designs for maximum safety (according to the von Mises yield condition) are determined along with these solutions for elastic design. The carrying capacity of the optimal plate is found to exceed that of the equal volume plate of constant thickness by 67% and 92% respectively for the simply-supported and clamped boundaries.

Yielding of oriented poly(vinyl chloride)

Abstract: Poly(vinyl chloride) sheet was oriented by hot drawing. The yield behavior of the oriented sheet was then investigated under uniaxial tension at room temperature as a function of the angle between the tensile axis and the molecular alignment direction. The onset of yield was localized in deformation bands. The variation of yield stress with direction and the direction in which the deformation bands formed were found to be satisfactorily accounted for in terms of a yield criterion based on that of von Mises, provided that a term representing internal compressive stress in the molecular alignment direction was included. The internal stress was found to increase from zero with increasing draw ratio of the prior hot drawing. It is pointed out that other workers have found polymers to obey the yield criterion of Coulomb rather than that of von Mises.

Finite element analysis of a bone healing model: 1-year follow-up after internal fixation surgery for femoral fracture.

Abstract: OBJECTIVE Finite element analysis was used to compare preoperative and postoperative stress distribution of a bone healing model of femur fracture, to identify whether broken ends of fractured bone would break or not after fixation dislodgement one year after intramedullary nailing. Method s: Using fast, personalized imaging, bone healing models of femur fracture were constructed based on data from multi-slice spiral computed tomography using Mimics, Geomagic Studio, and Abaqus software packages. The intramedullary pin was removed by Boolean operations before fixation was dislodged. Loads were applied on each model to simulate a person standing on one leg. The von Mises stress distribution, maximum stress, and its location was observed. Results : According to 10 kinds of display groups based on material assignment, the nodes of maximum and minimum von Mises stress were the same before and after dislodgement, and all nodes of maximum von Mises stress were outside the fracture line. The maximum von Mises stress node was situated at the bottom quarter of the femur. The von Mises stress distribution was identical before and after surgery. Conclusion : Fast, personalized model establishment can simulate fixation dislodgement before operation, and personalized finite element analysis was performed to successfully predict whether nail dislodgement would disrupt femur fracture or not.

Stress Around A Wellbore

Abstract: A study was made of the stress state in a porous elastic body, with particular emphasis on variations in selected failure criteria. The objective was to relate predicted changes in stress and failure criteria with fracture initiation experienced in certain forms of lost circulation, as opposed to hydraulic fracture extension. The 3 principal stresses at the well bore were expressed as functions of well-bore pressure; in addition, values of 8 additional parameters were varied over realistically expected ranges to determine their possible importance on the principal stresses. These 8 parameters were the 3 tectonic stresses, formation fluid pressure, pore pressure at the wall, Poisson's ratio, the ratio of unjacketed to jacketed rock compressibilities, and position around the well bore. Two failure criteria, the maximum principal stress and Von Mises number, were determined for the well stress condition chosen. Calculated results show that small changes (5%) in tectonic stresses can cause larger changes in well-bore stress (and potential failure) than very large (100%) changes in Poisson's or compressibility ratios.

Experimental evaluation of incremental theories for nonproportionate loading of thin-walled cylinders: Results of investigation indicate that while the Mises-Mises theory predicts good results for proportionate loading, it leaves much to be desired in predicting results for nonproportionate loading

Abstract: An experimental investigation was undertaken to evaluate incremental-strain theories which have been proposed in the literature to predict the loads on thin-walled cylinders subjected to nonproportionate loading which follow prescribed strain histories. Test data were obtained for two materials, annealed SAE 1035 steel and normalized 4340 steel. Material-property tests for the SAE 1035 steel indicated that the stress-strain diagram was flat topped and the material followed the Tresca flow condition. Similar tests for the SAE 4340 steel indicated that this steel was a linear strain-hardening material that followed the von Mises flow condition.

Elastic-plastic analysis of pressure vessel components

Abstract: : The report presents a survey on the use of digital computers for elastic-plastic analysis of pressure vessel components Included is a review of linear incremental stress strain relations for a strain hardening Prandtl-Reuss material with a von Mises yield criterion and the formation of generalized stress strain relations Case studies are given of axisymmmetric elastic- plastic analysis of a torispherical pressure vessel, a flush cylindrical nozzle in a sphere and a thick-walled cylinder under internal pressure

Generalized stress/strain rate relations for creep of thin shells; a comparison of “exact” and approximate relations

Abstract: A set of approximate generalized stress/strain rate relations which has been used for the stationary creep analysis of thin shells is compared with the corresponding ‘exact’ relations. The comparison is made by computing the functions from which the relations are derived and plotting the corresponding surfaces. Results are included for a limiting condition in which the stress/strain rate relations become those for a rigid-plastic material obeying the von Mises yield condition and associated flow rule. Although the comparison is made only for conditions valid in a cylindrical shell under rotationally symmetric loading, it indicates the errors which are likely to occur when the approximate relations are used in stationary creep analysis.

Anisotropic Yield Criterion under the Maximum Shear Stress Theory

Abstract: Yield criterion of anisotropic materials is developed under the maximum shearing stress hypothesis when the elements of materials are acted upon by three normal stresses in the direction of principal axes of anisotropy and a shearing stress around one of them. It is found for isotropic materials that the yield surface can be represented by two elliptical cone surfaces and a cylindroid one in the stress co-ordinate which is composed of the π-plane and its normal as a shearing stress. Under the assumption that these surfaces are independently distorted, translated and rotated, the numarical yield surface of anisotropic materials is found to be in good agreement with the experimental results of plates in any direction other than the direction of the degrees of angle, 60° to 70° form initial path of tensile prestrain.