A Variational Upper-Bound Method for Plane Strain Problems

1996 ◽  
Vol 118 (3) ◽  
pp. 301-309 ◽  
Author(s):  
Wei-Ching Yeh ◽  
Yeon-Sheng Yang
Keyword(s):  
Boundary Conditions ◽  
Upper Bound ◽  
Metal Flow ◽  
Variational Calculus ◽  
Experimental Result ◽  
Natural Boundary ◽  
Rigid Plastic ◽  
Upper Bound Method ◽  
Natural Boundary Conditions

In this paper, a variational upper-bound (VUB) method is proposed. It is the method that determines an upper-bound solution using variational calculus. By using the method, a set of so called “naturally boundary conditions,” which were all ignored in past investigations, can be theoretically derived for the rigid/plastic interface assumed to be arbitrary function in prior. This method is shown to be applicable to the cup ironing problem. From the result we can clearly indicate the role of these natural boundary conditions which reasonably account for the effect of friction on the pattern of metal flow. The VUB method not only presents an improvement on the traditional upper-bound method, but also favorably agrees with experimental result of Nielsen et al. (1963) in calculating upper-bound energy.

DIFFRACTION BY EDGES

2008 ◽  
Vol 22 (23) ◽  
pp. 2287-2328 ◽  
Author(s):  
ANDRÁS VASY
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Boundary Conditions ◽  
A Priori ◽  
Differential Forms ◽  
Natural Boundary ◽  
Propagation Of Singularities ◽  
Natural Boundary Conditions ◽  
Manifolds With Corners

In these expository notes we explain the role of geometric optics in wave propagation on domains or manifolds with corners or edges. Both the propagation of singularities, which describes where solutions of the wave equation may be singular, and the diffractive improvement under non-focusing hypotheses, which states that in certain places the diffracted wave is more regular than a priori expected, is described. In addition, the wave equation on differential forms with natural boundary conditions, which in particular includes a formulation of Maxwell's equations, is studied.

scholarly journals Elements of Bi-cubic Polynomial Natural Spline Interpolation for Scattered Data: Boundary Conditions Meet Partition of Unity Technique

2020 ◽  
Vol 8 (4) ◽  
pp. 994-1010
Author(s):  
Weizhi Xu
Keyword(s):  
Boundary Conditions ◽  
Spline Interpolation ◽  
Partition Of Unity ◽  
Scattered Data ◽  
Rectangular Domain ◽  
Natural Boundary ◽  
Natural Spline ◽  
Cubic Polynomial ◽  
Natural Boundary Conditions ◽  
Cubic Polynomials

This paper investigates one kind of interpolation for scattered data by bi-cubic polynomial natural spline, in which the integral of square of partial derivative of two orders to x and to y for the interpolating function is minimal (with natural boundary conditions). Firstly, bi-cubic polynomial natural spline interpolations with four kinds of boundary conditions are studied. By the spline function methods of Hilbert space, their solutions are constructed as the sum of bi-linear polynomials and piecewise bi-cubic polynomials. Some properties of the solutions are also studied. In fact, bi-cubic natural spline interpolation on a rectangular domain is a generalization of the cubic natural spline interpolation on an interval. Secondly, based on bi-cubic polynomial natural spline interpolations of four kinds of boundary conditions, and using partition of unity technique, a Partition of Unity Interpolation Element Method (PUIEM) for fitting scattered data is proposed. Numerical experiments show that the PUIEM is adaptive and outperforms state-of-the-art competitions, such as the thin plate spline interpolation and the bi-cubic polynomial natural spline interpolations for scattered data.

Meshless Integral Method for Analysis of Elastoplastic Geotechnical Materials

2010 ◽  
Author(s):  
Jianfeng Ma ◽  
Joshua David Summers ◽  
Paul F. Joseph
Keyword(s):  
Boundary Conditions ◽  
Function Approximation ◽  
Integral Method ◽  
Weak Form ◽  
Constitutive Law ◽  
Governing Equations ◽  
Natural Boundary ◽  
Pressure Sensitive ◽  
Support Domain ◽  
Natural Boundary Conditions

The meshless integral method based on regularized boundary equation [1][2] is extended to analyze elastoplastic geotechnical materials. In this formulation, the problem domain is clouded with a node set using automatic node generation. The sub-domain and the support domain related to each node are also generated automatically using algorithms developed for this purpose. The governing integral equation is obtained from the weak form of elastoplasticity over a local sub-domain and the moving least-squares approximation is employed for meshless function approximation. The geotechnical materials are described by pressure-sensitive multi-surface Drucker-Prager/Cap plasticity constitutive law with hardening. A generalized collocation method is used to impose the essential boundary conditions and natural boundary conditions are incorporated in the system governing equations. A comparison of the meshless results with the FEM results shows that the meshless integral method is accurate and robust enough to solve geotechnical materials.

Studies in collapse analysis of rigid-plastic plates with a square yield diagram

1957 ◽  
Vol 241 (1226) ◽  
pp. 311-338 ◽  
Keyword(s):  
Reinforced Concrete ◽  
Boundary Conditions ◽  
Upper Bound ◽  
Plastic Plate ◽  
Rigid Plastic ◽  
Concentrated Load ◽  
Arbitrary Boundary ◽  
Loaded Plate ◽  
Concrete Plate ◽  
Collapse Analysis

The collapse loads and mechanisms of a rigid-plastic plate with a square yield diagram, such as continuously reinforced concrete plate, are considered. Particular attention is paid to the case of a single concentrated load applied to a plate of arbitrary plan and with arbitrary boundary conditions. Upper-bound solutions are also given for a uniformly loaded plate of regular polygonal plan.

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