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
This paper proposes a novel numerical solution approach for the kinematic shakedown analysis of strain-hardening thin plates using the C^(1)nodal natural element method(C^(1)nodal NEM).Based on Koiter’s theorem and t...This paper proposes a novel numerical solution approach for the kinematic shakedown analysis of strain-hardening thin plates using the C^(1)nodal natural element method(C^(1)nodal NEM).Based on Koiter’s theorem and the von Mises and two-surface yield criteria,a nonlinear mathematical programming formulation is constructed for the kinematic shakedown analysis of strain-hardening thin plates,and the C^(1)nodal NEM is adopted for discretization.Additionally,König’s theory is used to deal with time integration by treating the generalized plastic strain increment at each load vertex.A direct iterative method is developed to linearize and solve this formulation by modifying the relevant objective function and equality constraints at each iteration.Kinematic shakedown load factors are directly calculated in a monotonically converging manner.Numerical examples validate the accuracy and convergence of the developed method and illustrate the influences of limited and unlimited strain-hardening models on the kinematic shakedown load factors of thin square and circular plates.展开更多
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
Nanoplates have been widely used as elementary components for ultrasensitive and ultrafine resolution applications in the field of nano-electro-mechanical systems because of their potentially remarkable mechanical pro...Nanoplates have been widely used as elementary components for ultrasensitive and ultrafine resolution applications in the field of nano-electro-mechanical systems because of their potentially remarkable mechanical properties.The accurate analysis of their mechanical behavior is currently of particular interest in the function design and reliability analysis of nano-scaled devices.To examine the size-dependent bending and vibration behavior of nanoplates with curvilinear and irregular shapes,a new p-version curved C^(1)finite element is formulated in the framework of the nonlocal Kirchhoff plate model.This newly developed element not only enables an accurate geometry representation and easy mesh generation of curvilinear domains but also overcomes the difficulty of imposing C^(1)conformity required by the nonlocal Kirchhoff plate model,particularly on the curvilinear inter-element boundaries.Numerical examples show that this element can produce an exponential rate of convergence even when curved elements are used in the domain discretization.Vast numerical results are presented for nanoplates with various geometric shapes,including rectangular,circular,elliptic,annular,and sectorial.The high accuracy of the present element is verified by comparing the obtained results with analytical and numerical results in the literature.Additionally,a comprehensive parametric analysis is conducted to investigate the influences of nonlocal parameters,plate dimensions,and boundary conditions on the nonlocal behavior of nanoplates.The present element can be envisaged to allow large-scale mechanical simulations of nanoplates,with a guarantee of accuracy and efficiency.展开更多
The classical problem of the construction of C^1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method.In order to achieve the ...The classical problem of the construction of C^1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method.In order to achieve the C^1 conformity on the interfaces of quadrilateral elements,complete second-order derivatives are used at the element vertices,and the information of geometrical mapping is also considered into the construction of shape functions.It is found that the shape functions and the polynomial spaces of the present elements vary with element shapes.However,the developed quadrilateral elements are at least third order for general quadrilateral shapes and fifth order for rectangular shapes.Therefore,very fast convergence can be achieved.A promising feature of the present elements is that they can be used in cooperation with those high-precision rectangular and triangular elements.Since the present elements are over conforming on element vertices,an approach for handling problems of material discontinuity is also proposed.Numerical examples of Kirchhoff plates are employed to demonstrate the computational performance of the present elements.展开更多
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.
基金supported by the Chinese Postdoctoral Science Foundation(2013M540934).
文摘This paper proposes a novel numerical solution approach for the kinematic shakedown analysis of strain-hardening thin plates using the C^(1)nodal natural element method(C^(1)nodal NEM).Based on Koiter’s theorem and the von Mises and two-surface yield criteria,a nonlinear mathematical programming formulation is constructed for the kinematic shakedown analysis of strain-hardening thin plates,and the C^(1)nodal NEM is adopted for discretization.Additionally,König’s theory is used to deal with time integration by treating the generalized plastic strain increment at each load vertex.A direct iterative method is developed to linearize and solve this formulation by modifying the relevant objective function and equality constraints at each iteration.Kinematic shakedown load factors are directly calculated in a monotonically converging manner.Numerical examples validate the accuracy and convergence of the developed method and illustrate the influences of limited and unlimited strain-hardening models on the kinematic shakedown load factors of thin square and circular plates.
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the National Major Science and Technology Projects of China(Grant No.J2019-VI-0001-0114)the National Natural Science Foundation of China(Grant Nos.11972004,11772031,11402015)。
文摘Nanoplates have been widely used as elementary components for ultrasensitive and ultrafine resolution applications in the field of nano-electro-mechanical systems because of their potentially remarkable mechanical properties.The accurate analysis of their mechanical behavior is currently of particular interest in the function design and reliability analysis of nano-scaled devices.To examine the size-dependent bending and vibration behavior of nanoplates with curvilinear and irregular shapes,a new p-version curved C^(1)finite element is formulated in the framework of the nonlocal Kirchhoff plate model.This newly developed element not only enables an accurate geometry representation and easy mesh generation of curvilinear domains but also overcomes the difficulty of imposing C^(1)conformity required by the nonlocal Kirchhoff plate model,particularly on the curvilinear inter-element boundaries.Numerical examples show that this element can produce an exponential rate of convergence even when curved elements are used in the domain discretization.Vast numerical results are presented for nanoplates with various geometric shapes,including rectangular,circular,elliptic,annular,and sectorial.The high accuracy of the present element is verified by comparing the obtained results with analytical and numerical results in the literature.Additionally,a comprehensive parametric analysis is conducted to investigate the influences of nonlocal parameters,plate dimensions,and boundary conditions on the nonlocal behavior of nanoplates.The present element can be envisaged to allow large-scale mechanical simulations of nanoplates,with a guarantee of accuracy and efficiency.
基金supported by the National Natural Science Foundation of China(Grant Nos.11402015,11872090&11672019)。
文摘The classical problem of the construction of C^1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method.In order to achieve the C^1 conformity on the interfaces of quadrilateral elements,complete second-order derivatives are used at the element vertices,and the information of geometrical mapping is also considered into the construction of shape functions.It is found that the shape functions and the polynomial spaces of the present elements vary with element shapes.However,the developed quadrilateral elements are at least third order for general quadrilateral shapes and fifth order for rectangular shapes.Therefore,very fast convergence can be achieved.A promising feature of the present elements is that they can be used in cooperation with those high-precision rectangular and triangular elements.Since the present elements are over conforming on element vertices,an approach for handling problems of material discontinuity is also proposed.Numerical examples of Kirchhoff plates are employed to demonstrate the computational performance of the present elements.