This paper proposes a numerical solution method for upper bound shakedown analysis of perfectly elasto-plastic thin plates by employing the C^(1) natural element method.Based on the Koiter’s theorem and von Mises yie...This paper proposes a numerical solution method for upper bound shakedown analysis of perfectly elasto-plastic thin plates by employing the C^(1) natural element method.Based on the Koiter’s theorem and von Mises yield criterion,the nonlinear mathematical programming formulation for upper bound shakedown analysis of thin plates is established.In this formulation,the trail function of residual displacement increment is approximated by using the C^(1) shape functions,the plastic incompressibility condition is satisfied by introducing a constant matrix in the objective function,and the time integration is resolved by using the Konig’s technique.Meanwhile,the objective function is linearized by distinguishing the non-plastic integral points from the plastic integral points and revising the objective function and associated equality constraints at each iteration.Finally,the upper bound shakedown load multipliers of thin plates are obtained by direct iterative and monotone convergence processes.Several benchmark examples verify the good precision and fast convergence of this proposed method.展开更多
C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolati...C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.展开更多
基金supported by the Chinese Postdoctoral Science Foundation(2013M540934)supported by the National Key Research and Development Program of China(2016YFC0801905,2017YFF0210704).
文摘This paper proposes a numerical solution method for upper bound shakedown analysis of perfectly elasto-plastic thin plates by employing the C^(1) natural element method.Based on the Koiter’s theorem and von Mises yield criterion,the nonlinear mathematical programming formulation for upper bound shakedown analysis of thin plates is established.In this formulation,the trail function of residual displacement increment is approximated by using the C^(1) shape functions,the plastic incompressibility condition is satisfied by introducing a constant matrix in the objective function,and the time integration is resolved by using the Konig’s technique.Meanwhile,the objective function is linearized by distinguishing the non-plastic integral points from the plastic integral points and revising the objective function and associated equality constraints at each iteration.Finally,the upper bound shakedown load multipliers of thin plates are obtained by direct iterative and monotone convergence processes.Several benchmark examples verify the good precision and fast convergence of this proposed method.
基金supported by the SDUST Spring Bud (2009AZZ021)Taian Science and Technology Development (20112001)
文摘C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.
