Post-buckling behaviour of elastic circular plates using a simple finite element formulation

The post-buckling behaviour of elastic circular plates is studied in this paper using a simple finite element formulation. The final linearized eigenvalue problem is solved by using three numerical methods and all these methods are found to yield accurate results for moderately large deflections. Comparison of the present results with the results existing in literature shows the validity of this formulation.     

Design of a planar multibody dynamic system with ANCF beam elements based on an element-wise stiffness evaluation procedure

The absolute nodal coordinate formulation (ANCF) has been widely applied for large deformation analysis in flexible multibody dynamics. Although the formulation led to stable solutions for time integration under large rotations and deformations, excessive time consumption was recorded. The nonlinear relationship between the deformation and the internal force accounted for repeated adjustment to the force equilibrium state as the structure deformed. In this research, an equivalent model of the ANCF beam structure was constructed. The stiffness evaluation method was applied in an element-wise manner. In this model, the irrelevant parts were separated from those that relate to the displacements and design parameters enabling efficient updates of internal forces to achieve force equilibrium. Therefore, by using this model, optimization problems, in which displacements as well as design parameters keep changing can be efficiently approached. To verify the proposed method, two examples of optimization problems related to a free-falling pendulum and a slider-crank mechanism are demonstrated.     

轴向力在线监控装置弹性元件的有限元分析

对离心式旋转机械轴向力在线监控装置做了简单的介绍,此装置包括测力弹性元件和轴向力在线监控 系统两部分,为了保证所研制的测力传感器的性能,采用有限元方法计算了弹性元件在轴向力 Ｆ＝ ３９．２ ｋＮ时 的应变、应力、灵敏度及轴位移的分布情况,结果表明：所设计的测力传感器完全符合要求。     

A reinvestigation of post-buckling behaviour of elastic circular plates using a simple finite element formulation

A modified finite element formulation to study the post-buckling behaviour of elastic circular plates is presented in this paper. A discussion on the derivation of nonlinear stiffness matrix for post-buckling analysis is included and the present results are compared with continuum solutions.     

Stability of plates using a mixed finite element formulation

A rectangular plate finite element is developed according to a variational principle due to Prager The element is applied to plate stability analysis. The results obtained compare very favorably with results based on previous formulations.     

A quadratically convergent procedure for the calculation of stability points in finite element analysis

In this paper a new finite element formulation is given for the analysis of nonlinear stability problems. The introduction of extended systems opens the possibility to compute limit and bifurcation points directly. Here, the use of the directional derivative yields a quadratically convergent iteration scheme. The combination with arc-length and branch-switching procedures leads to a global algorithm for path-following.     

A simple and efficient beam element for the combined nonlinear analysis of frameworks

A materially and geometrically nonlinear three-dimensional beam element is discussed. The element is first derived in the small deflection elasto-plastic range and then further studied to incorporate finite deflection effects in a simplified way. The performance of the element is tested by two nonlinear examples and the scope of its use for the nonlinear analysis of multi-member space structures is discussed.     

Reduction of system matrices of planar beam in ANCF by component mode synthesis method

A method of reducing the system matrices of a planar flexible beam described by an absolute nodal coordinate formulation (ANCF) is presented. In this method, we focus that the bending stiffness matrix expressed by adopting a continuum mechanics approach to the ANCF beam element is constant when the axial strain is not very large. This feature allows to apply the Craig–Bampton method to the equation of motion that is composed of the independent coordinates when the constraint forces are eliminated. Four numerical examples that compare the proposed method and the conventional ANCF are demonstrated to verify the performance and accuracy of the proposed method. From these examples, it is verified that the proposed method can describe the large deformation effects such as dynamic stiffening due to the centrifugal force, as well as the conventional ANCF does. The use of this method also reduces the computing time, while maintaining an acceptable degree of accuracy for the expression characteristics of the conventional ANCF when the modal truncation number is adequately employed. This reduction in CPU time particularly pronounced in the case of a large element number and small modal truncation number; the reduction can be verified not only in the case of small deformation but also in the case of a fair bit large deformation.     

An efficient formulation for flexible multibody dynamics using a condensation of deformation coordinates

Multibody System Dynamics - In this work a new approach to deal with non-ideal operative aspects of spatial revolute joints by means of a three-dimensional finite element analysis (3D-FEA) is...     

Numerical solutions of the one-phase classical Stefan problem using an enthalpy green element formulation

The enthalpy method is exploited in tackling a heat transfer problem involving a change of state. The resulting governing equation is then solved with a hybrid finite element - boundary element technique known as the Green element method (GEM). Two methods of approximation are employed to handle the time derivative contained in the discrete element equation. The first involves a finite difference method, while the second utilizes a Galerkin finite element approach. The performance of both methods are assessed with a known closed form solution. The finite element based time discretization, despite its greater challenge, yields less reliable numerical results. In addition a numerical stability test of both methods based on a Fourier series analysis explain the dispersive characters of both techniques, and confirms that replication of correct results is largely attributed to their ability to handle the harmonics of small wavelengths which are usually dominant in the vicinity of a front.     

Accurate and efficient nonlinear formulation of a nine-node shell element with spurious mode control

A nine-node Lagrangian shell finite element is presented for full nonlinear analysis of shell-type structures. The formulation is based on the assumption of large displacements, finite rotations, and small strains. The major focus is on the robustness, accuracy, and efficiency of the finite element. Uniform reduced (2 x 2) quadrature is used for evaluation of the element stiffness and recovery of element nodal forces, and an improved ‘ projection operator ’ procedure is employed for stabilization of the resulting spurious zero-energy modes. Efficient techniques are described for calculation of shape function derivatives, performance of local-to-global transformations, and determination of the ‘ stabilization coefficients ’ of the artificial mode control procedure. Numerical integration is employed through the thickness of the element for accurate evaluation of the plastic response in moderately thick shells. The projection operator employed for the mode stabilization is orthogonal to constant, linear, and quadratic displacement fields in the local Cartesian (x′, y′) coordinates at each of the 2 × 2 Gauss quadrature stations. As a result, the flat-plate pure-bending patch tests are not affected for arbitrary element sizes. The resulting element is essentially free of membrane and shear locking problems, and it has not shown any signs of spurious zero energy mode effects for a large number of linear and nonlinear tests.     

Stability of cylindrical shell panels subjected to follower forces based on a mixed finite element formulation

A mixed finite element formulation is developed from a weak variational priniciple. This formulation is applied to stability analysis of cylindrical shell structures subjected to follower loading. Bilinear trial functions are used for all field variables. The rectangular curved elements presented here satisfy the continuity requirements for the field variables at the element interface. Two examples of a cantilevered cylindrical shell panel under different kinds of loading are solved.     

Development of constrained control allocation for ship berthing by using autonomous tugboats

International Journal of Control, Automation and Systems - In this paper, we propose a new approach to ship berthing by using autonomous tugboats. This approach overcomes the nominal effectiveness...     

有限元法的轴向运动梁的激励功率谱辨识

主要考虑弯曲变形的细长轴向运动梁,可以作为工程中广泛应用在航天器天线、液体输送管道、汽车驱动带、电梯缆索等的简化机构.对轴向运动柔性梁线性微分方程,采用复模态分析方法导出两端简支和固支边界条件下的固有频率方程;采用Ritz法建立轴向运动梁的有限单元法模型.基于该模型在多种边界条件下进行梁的横向振动分析,并开展定点激励下激励功率谱的辨识.仿真结果表明,与传统的Galerkin截断方法相比.有限元方法能够克服分析方法的建模困难,对复杂边界梁进行有效的分析,对激励的功率谱能够有效地辨识.     

Finite element analysis of geometrically nonlinear plate behaviour using a mindlin formulation

The paper presents a finite element analysis of the geometrically nonlinear behaviour of plates using a Mindlin formulation with the assumption of small rotations. A comparison of the performance of Linear, Serendipity, Lagrangian and Heterosis elements is given for square, skew, circular and elliptical plates subjected to distributed and point loading. All results are presented numerically. Generally the higher order elements give good results although no particular element emerges as being “best”.     

Postbuckling analysis of plates on an elastic foundation by the boundary element method

The postbuckling behavior of plates on an elastic foundation is studied by using the boundary element method (BEM). A new fundamental solution of lateral deflection is derived through the resolution theory of a differential operator, and a set of boundary element formulae in incremental form is presented. By using these formulae, the BEM solution procedure becomes relatively simple. The results of a number of numerical examples are compared with existing solutions and good agreement is observed. It shows that the proposed method is effective for solving the postbuckling problems of plates with arbitrary shape and various boundary conditions.     

Mathematical formulation and a new metaheuristic for the constrained double-floor corridor allocation problem

A layout plan for a manufacturing system that is designed without any facility constraints will most likely be infeasible when confronted with reality. Additionally, considering that land available for building industrial plants is limited and its cost is high, it is necessary to investigate the layout planning of two and multi-floor facilities. To address these shortages in the scientific literature, we focus on the double-floor corridor allocation problem (DFCAP) which covers a wide range of complex facility constraints, such as fixed floor constraints, fixed row constraints, fixed positioning constraints, mutual floor constraints, mutual row constraints, sequencing constraints and adjacency constraints. For the model mentioned above, we term it as a constrained DFCAP (cDFCAP). A mixed-integer linear programming model is formulated for the cDFCAP. In order to solve larger realistic problems, a constrained metaheuristic with the memetic algorithm framework customised for solving the cDFCAP is introduced in this work. In our algorithm, four problem-specific heuristic rules to construct a set of initial solutions are developed. In addition, an ideal parameter combination for our constrained memetic algorithm is determined through a Taguchi experimental design. Finally, the results of a set of cDFCAP instances with different sizes (n = 10∼80) report that our provided approach is effective for the considered problem.     

Identification of nonlinear elastic solids by a finite element method

The problem of utilizing experimental data to characterize the stress constitutive function for a nonlinear elastic solid is formulated as an inverse boundary value problem. The use of finite element discretization is extended by introducing a technique of material parameterization that utilizes finite elements defined over the domain of the stress constitutive function. The discretized identification problem is then reduced to a system of nonlinear algebraic equations that couples the data set and the discretized boundary value problem. The effect of errors in measured data is minimized by employing a weighted least squares error norm to generate the equations from which the unknown material parameters are obtained. An illustrative numerical experimental is included.     

Development of a system usability assessment procedure using oculo-motors for input operation

This paper investigates the relationship between oculo-motors, such as eye-movement and pupillary change, and the conventional subjective “usability” index, using time-domain and frequency-domain approaches, with the objective to determine the possibility of evaluating interaction through oculo-motors. An evaluation experiment was conducted by operating a target on a computer display using mouse, keyboard and key pad as input devices. The results show that there is a significant correlation between pupil size and SU-score, which is an established subjective evaluation index for system usability. Cross spectrum densities (CSD) between horizontal and vertical eye-movements and coherence as standardized CSD also significantly correlate with the results of the SU-scores and error rates. To determine the frequency range of CSD and coherence for usability assessment, frequency components used as factors were extracted using factor analysis. According to the correlation coefficients between these and the performance of factor scores for predicting the conventional metrics, factor scores of CSD are better indices for assessing usability than factor scores of coherence. These two results suggest that pupil size and index of eye-movement as oculo-motor indices based on time-domain and frequency-domain approaches can provide information about a system’s overall usability regarding the input operation task.