The curved beam element and its convergence rate

The quasi-conforming element of the curved beam and shallow curved beam is given in this paper. Numerical examples illustrate that the quasi-conforming elements of the curved beam and shallow curved beam which is used to approximate the curved beam have better accuracy than the straight beam element. The curved beam element constructed by displacement method can not satisfy rigid body motion condition and the very fine grids have to be used in order to satisfy rigid body motion condition approximately.In this paper it is proved that the straight beam element and the quasi-conforming element of the curved beam and shallow curved beam, when element size is reduced infinitely, have convergence rate with the same order O(l²) and when regular elements are used l is the element length.The Project Supported by National Natural Science Foundation of China.     

A Comment on the Low Speed Impact of a Clamped Beam by a Heavy Striker∗

ABSTRACT

An approximate theoretical analysis is presented for a rigid, perfectly plastic clamped beam struck transversely at the mid-span by a mass which produces Finite transverse displacements. An alternative quasi-static procedure is proposed for estimating the dynamic plastic response of a beam when struck by a heavy mass that travels at a low speed. The theoretical basis of this method is explained and the accuracy is examined by an error analysis. Finally, it is suggested that this quasi-static procedure could be used for estimating the dynamic plastic response of other structures that are struck by a heavy mass traveling at a low speed,     

Collapse Loads of a Cylindrical or Toroidal Free-Standing Inflatable Membrane∗

ABSTRACT

The behavior of free-standing cylindrical or toroidal membranes under collapse loads is analyzed in this paper. Results developed here agree with experiments and previous analysis and show that the mechanism of collapse of such membranes consists in the appearance of local, large deformed zones called pneumatic hinges, whereas the rest of the membrane remains unaffected and behaves like a rigid or elastic body.     

Application of a Special Yield Stress Strain Rate Law to Structural Impulse Problems

ABSTRACT

This paper presents approximate solutions to the dynamic response of three impulsively loaded structures: a wire with an impulsively loaded end mass, an impulsively loaded circular ring, and a cantilever beam with a tip mass subjected to an impulsive load at its tip. The material is assumed to be rigid, perfectly plastic with strain rate sensitivity. A proposed power law form of yield stress strain rate relationship is used to simplify the theoretical development. Numerical solutions are presented for mild steel and are compared with previously published results. Elastic effects and wave propogations are ignored.     

Accuracy Analysis of the Semi-Analytical Method for Shape Sensitivity Calculation∗

ABSTRACT

The semi-analytical method of design sensitivity analysis that is widely used for calculating derivatives of static response with respect to design variables for structures modeled by finite elements is studied in this paper. It is shown that the method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. Errors are shown to be associated with an incompatibility of the sensitivity field with the structure. An error index is developed to test the accuracy of the semi-analytical method. It characterizes the difference in errors between a general finite difference method and the semi-analytical method. A method for improving the accuracy of the semi-analytical method (when possible) is provided. Examples are presented to demonstrate the use of the error index.     

Concentrated Loads on Light Gauge Steel Diaphragms

ABSTRACT

When a point load is applied within the length of a side of a diaphragm, significant local forces may arise. A theory is developed whereby both the forces induced in the edge fasteners and the bending moments induced in the edge members may be evaluated from simple explicit expressions. This theory is verified by comparison with finite element investigations.

The behavior of sheeting in compression surrounding edge fasteners is investigated experimentally and a simple approach to the resulting buckling failure is derived. Finally, some tests on complete diaphragm assemblies subject to compressive concentrated loads are described and the results compared with the theory.     

Large Deflection of a Circular Plate on Elastic Foundation under Symmetrical Load

ABSTRACT

The large deflection of a clamped circular plate on elastic foundation under nonuniform but symmetrical loads has been investigated following Berger's approximate method. The deflections are obtained in the form of an infinite series involving Bessel functions. Graphs are plotted for deflections, bending moments, and bending stresses for various values of foundation modulus and load functions.     

Design Component Method for Sensitivity Analysis of Built-up Structures

ABSTRACT

A “design component method” that provides a unified and systematic organization of design sensitivity analysis for built-up structures is developed and implemented. Both conventional design variables, such as thickness and cross-sectional area, and shape design variables of components of built-up structures are considered. It is shown that design of components of built-up structures can be characterized and system design sensitivity expressions obtained by simply adding contributions from each component. The method leads to a systematic organization of computations for design sensitivity analysis that is similar to the way in which computations are organized within a finite element code.     

初始纵横向荷载效应对薄板自振频率的影响分析The analysis for the effect of both initial in-plane and transverse loads on the natural frequency of plates

首先基于能量变分原理,给出了同时考虑初始纵向、横向荷载效应情况下板的应变能表达、动力平衡微分方程及单元刚度矩阵。再以动力平衡微分方程为基础,运用伽辽金法解得四种典型板同时考虑初始纵向、横向荷载效应的基频近似解,并运用瑞利法解得简支矩形板考虑初始纵向、横向荷载效应的前三阶频率近似解。然后相互验证了考虑初始纵向、横向荷载效应的板单元刚度矩阵和频率近似解的正确性,并进一步分析了初始纵向、横向荷载及相关因素对板自振频率的影响。结果表明,考虑初始纵向、横向荷载效应后,板的自振频率主要受初始纵向荷载、初始横向荷载、板的厚度及边界条件等因素的影响;初始纵向、横向荷载效应对板的基频影响明显于高阶频率;初始纵向、横向荷载对板的自振频率影响分别呈线性和抛物线规律。     

Evolution of a heavy rigid body rotation under the action of unsteady restoring and perturbation torques

The paper develops an approximate solution to the system of Euler’s equations with additional perturbation term for dynamically symmetric rotating rigid body. The perturbed motions of a rigid body, close to Lagrange’s case, under the action of restoring and perturbation torques that are slowly varying in time are investigated. We describe an averaging procedure for slow variables of a rigid body perturbed motion, similar to Lagrange top. Conditions for the possibility of averaging the equations of motion with respect to the nutation phase angle are presented. The averaging technique reduces the system order from 6 to 3 and does not contain fast oscillations. An example of motion of the body using linearly dissipative torques is worked out to demonstrate the use of general equations. The numerical integration of the averaged system of equations is conducted of the body motion. The graphical presentations of the solutions are represented and discussed. A new class of rotations of a dynamically symmetric rigid body about a fixed point with account for a nonstationary perturbation torque, as well as for a restoring torque that slowly varies with time, is studied. The main objective of this paper is to extend the previous results for problem of the dynamic motion of a symmetric rigid body subjected to perturbation and restoring torques. The proposed averaging method is implemented to receive the averaging system of equations of motion. The graphical representations of the solutions are presented and discussed. The attained results are a generalization of our former works where µ and M_i are independent of the slow time τ and M_i depend on the slow time only.

     

平面刚架弹塑性大位移分析的多刚体离散元法

本文基于多刚体－弹簧系统模型，给出了求解平面刚架结构弹塑性、大位移极限承载力分析的多刚体离散元法。文中首先推导了多刚体离散元法在总体坐标下的切线刚度阵，建立多刚体离散元法的增量平衡方程；而后推导了多刚体离散元的弹塑性弹簧系数矩阵，建立了多刚体离散元内力屈服面塑性铰法的增量求解格式，成功地进行了平面钢框架的弹塑性、大位移极限承载力分析。计算结果与其他数值方法或实验结果吻合良好，显示了多刚体离散元方法进行结构极限承载力分析这一复杂问题的优越性     

Stability of Thin-Walled Open Beams Under Nonconservative Loads

ABSTRACT

A finite element formulation for free-vibration analysis of straight prismatic beams of general thin-walled open cross-section, under conservative and nonconservative loads, is presented. The formulation is used to calculate the flutter load for a number of beam problems and is verified by comparison with pre-existing numerical solutions.     

Investigation of the Effects of Environmental Fatigue on the Mechanical Properties of GFRP Composite Constituents Using Nanoindentation

Background

Fatigue failure criteria for fibre reinforced polymer composites used in the design of marine structures are based on the micromechanical behaviour (e.g. stiffness properties) of their constituents. In the literature, there is a lack of information regarding the stiffness degradation of fibres, polymer matrix and fibre/matrix interface regions affected by environmental fatigue.

Objective

The aim of present study is to characterize the stiffness properties of composite constituents using the nanoindentation technique when fatigue failure of composites is due to the combined effect of sea water exposure and cyclic mechanical loads.

Methods

In the present study, the nanoindentation technique was used to characterize the stiffness properties of composite constituents where the effects of neighbouring phases, material pile up and viscoplasticity properties of the polymer matrix are corrected by finite element simulation.

Results

The use of finite element simulation in conjunction with nanoindentation test data, results in more accurate estimation of projected indented area which is required for measuring the properties of composite constituents. In addition, finite element simulation provides a greater understanding of the stress transfer between composite constituents during the nanoindentation process.

Conclusions

Results of nanoindentation testing on the composite microstructure of environmentally fatigue failed composite test coupons establish a strong link to the stiffness degradation of the fiber/matrix interface regions, verifying the degradation of composite constituents identified by scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDX) analysis.

     

Application of the angular superposition method to the contact problem on the compression of an elastic cylinder

The angular superposition method is used to construct an approximate solution of the contact problem on the compression of an elastic cylinder by two rigid plates. The solution thus obtained has a closed-form analytic expression and can be used in the entire domain of the cylinder cross-section. We analyze the absolute error, which takes the largest value near the points of contact between the plates and the cylinder, where the boundary conditions are discontinuous. According to the von Mises criterion, when moving into the depth of the cylinder from the contact site along the symmetry axis, the second invariant J ₂ of the stress deviator tensor first decreases and then, after attaining a minimum, increases and attains the largest value at a small depth, which agrees with Johnson’s photoelastic experiments and Dinnik’s computations. We present the graphs of the displacement and normal stress distributions over the contact site, the dependence of the compressing force on the displacements of rigid plates, and the dependence of the invariant J ₂ on the coordinate along the symmetry axis. If 640 computation points are chosen on the cylinder boundary and the Hertz law for the normal pressure on the contact site is used, then the error in the approximate solution near the endpoint of the contact site is approximately 55%, and if the proposed two-parameter normal law is used, then the error is of the order of 4%. On the free lateral surface of the cylinder boundary, we find the critical pointM*, which separates the cylinder contraction and extension parts.The contact problems are the most difficult problems, and their solution is complicated by the discontinuous boundary conditions [1–5]. In [6], the contact problem is solved by the Fourier method, which can be used only for bodies of classical shapes. In such cases, the problem can be reduced to solving coupled integral equations [7]. The interaction between the bandage and a cylindrical body is considered in [2, 6, 7]. In [8], the possibility of using the finite element method is investigated in the case of contact problems for a differential wheel with roughness of the contacting surfaces taken into account. In [9, 10], the method of homogeneous solutions is used to consider contact problems for a finite-dimensional elastic cylinder loaded on its end surfaces. Note that only error estimates are given in the literature cited above; the absolute error over the entire domain of the elastic body is not studied, although this is one of the important characteristics of the obtained approximate solution. A sufficiently complete survey of the literature in the field of contact interactions of elastic bodies is given in [3–5].In what follows, we propose to solve contact problems by the angular superposition method [11]. This method can be used for bodies of nonclassical shapes, which can be multiply connected, and the friction on the contact site can be taken into account. In the present paper, as a first example of applied character, we show how this method can be used in the simplest case. The multiple connectedness and the curvilinearity of the shape of the body, as well as taking into account the friction on the boundary, do not create new essential difficulties in this method.     

Homoclinic Shadowing

A new method for rigorously establishing the existence of a transversal homoclinic orbit to a periodic orbit (or a fixed point) of diffeomorphisms in Rⁿ is presented. It is a computer-assisted technique with two main components. First, a global Newton’s method is devised to compute a suitable pseudo (approximate) homoclinic orbit to a pseudo periodic orbit. Then, a homoclinic shadowing theorem, which is proved herein, is invoked to establish the existence of a true transversal homoclinic orbit to a true periodic orbit near these pseudo orbits.     

The Explicit Expression of Internal Forces in Prismatic Membered Structures*

ABSTRACT

Analytic expressions for member forces in linear elastic redundant trusses have recently been given by the author. It was shown that the internal forces in a truss are the ratios of two multilinear homogeneous polynomials in the longitudinal stiffnesses of the elements of the structure. The order of the polynomials is equal to the number of nodal degrees of freedom of the structure. The number of terms of each polynomial is equal to the number of statically determinate stable substructures that can be derived from the original structure. It was shown that coefficients of the polynomials can be computed through the equilibrium equations and by enforcing global compatibility of deformations. This paper generalizes these results to the case of linear elastic structures, composed of uniform prismatic elements that have extensional, flexural, and torsional stiffness. This is done by replacing each bi-modal bending element with a unimodal moment element and a unimodal shear element. This allows the representation of deformation of the elements by six uncoupled basic deformation patterns in the case of structures in space, thus paving the way for truss-type analysis for general structures that are composed of uniform prismatic elements. As a result, multilinear polynomials that appear in expressions for stress resultants are the products of axial, bending, and torsional stiffnesses of subsets of the original structure. The number of terms appearing in the polynomials renders the exact analytic expressions intractable for practical engineering structures. However, the construct of the analytic equations may constitute a basis for writing approximate expressions for member forces in frames, explicitly in terms of rigidities of components of the structure. This paper describes such an approximate expression, with a reduced number of terms in the polynomials. The theory is illustrated with numerical examples of analysis of planar structures     

Prediction of Gear Dynamics Using Fast Fourier Transform of Static Transmission Error*

ABSTRACT

An analytical computer simulation procedure for dynamic modeling of low-contact-ratio spur gear systems is presented. The procedure computes the gear static transmission error and uses a Fast Fourier Transform (FFT) to generate its frequency spectrum at various tooth profile modifications. The dynamic loading response of an unmodified (perfect involut) gear pair is compared with that of gears with profile modifications. Correlations are found between several profile modifications and the resulting dynamic loads. An effective error, obtained from frequency domain anal     

Coupled free vibration analysis of a fluid-filled rectangular container with a sagged bottom membrane

In the present paper, two-dimensional coupled free vibrations of a fluid-filled rectangular container with a sagged bottom membrane are investigated. This system consists of two rigid walls and a membrane anchored along two rigid vertical walls. It is filled with incompressible and inviscid fluid. The membrane material is assumed to act like an inextensible material with no bending resistance. First, the nonlinear equilibrium equation is solved and the equilibrium shape of the membrane is obtained using an analytical formulation neglecting the membrane weight. The small vibrations about the equilibrium configuration are then investigated. Along the contact surface between the bottom membrane and the fluid, the compatibility requirement is applied for the fluid–structure interactions and the finite element method is used to calculate the natural frequencies and mode shapes of the fluid–membrane system. The vibration analysis of the coupled system is accomplished by using the displacement finite element for the membrane and the pressure fluid-finite element for the fluid domain. The variations of natural frequencies with the pressure head, the membrane length, the membrane weight and the distance between two rigid walls are examined. Moreover, the mode shapes of system are investigated.     

梁长对移动荷载下梁响应影响研究

本文研究了梁跨长对移动荷载下梁稳态响应的影响.在以往的研究中,通常采用Galerkin方法或者有限元方法计算不同长度的梁的动力响应.当梁长的增加不再明显改变梁的动力响应时,可认为梁此时的长度可以代替无穷长时的情况.采用上述方法的研究表明,当梁长大于10 m时,就可以用有限长梁近似无限长梁的响应.本文通过求解有限长梁和无...     

A Robust Finite Element-based Filter for Digital Image and Volume Correlation Displacement Data

Background

Digital Image and Volume Correlation (DIC and DVC) are non-contact measurement techniques that are used during mechanical testing for quantitative mapping of full-field displacements. The relatively high noise floor of DIC and DVC, which is exasperated when differentiated to obtain strain fields, often requires some form of filtering. Techniques such as median filters or least-squares fitting perform poorly over high displacement gradients, such as the strain localisation near a crack tip, discontinuities across crack flanks or large pores. As such, filtering does not always effectively remove outliers in the displacement field.

Objective

This work proposes a robust finite element-based filter that detects and replaces outliers in the displacement data using a finite element method-based approximation.

Methods

A method is formulated for surface (2D and Stereo DIC) and volumetric (DVC) measurements. Its validity is demonstrated using analytical and experimental displacement data around cracks, obtained from surface and full volume measurements.

Results

It is shown that the displacement data can be filtered in such a way that outliers are identified and replaced. Moreover, data can be smoothed whilst maintaining the nature of the underlying displacement field such as steep displacement gradients or discontinuities.

Conclusions

The method can be used as a post-processing tool for DIC and DVC data and will support the use of the finite element method as an experimental–numerical technique.