Optimal design of plastic cylindrical shells of von Mises material

Optimal design of plastic circular cylindrical shells of von Mises material is studied. The optimization problem is stated as the maximization problem of the load carrying capacity for given weight of the shell. Shells with constant and piecewise-constant thickness are considered. The maximization problem is performed under the requirement that the material volume of the stepped shell is equal to the case of the reference shell of constant thickness. The material of the shell is assumed to be an ideal rigid plastic obeying von Mises yield criterion. The considered nonlinear problems are solved by using the CASes method.     

Collapse of long, noncircular, cylindrical shells under pure bending

This paper describes an extension of a method developed in a previous paper to determine the moment carrying capacity of elastoplastic noncircular cylindrical shells with infinite length by the finite element method. As a result of the shape change in the cross section of a shell during deformation, the bending moment reaches a global maximum value and then decreases as the bending curvature further increases. The shell would consequently collapse at the maximum moment. However, a bifurcation buckling may occur before the maximum moment can be developed. This bifurcation buckling could induce collapse of the shell under a moment less than the maximum. Determination of the likelihood that the bifurcation buckling would generate shell collapse may be made from the initial post-buckling behavior. An initial post-buckling analysis based on the J₂ deformation theory of plasticity has been developed in this paper. The finite element method with one spatial variable is used to locate the bifurcation point as well as to analyze the initial post-buckling behavior. Numerical examples of cylindrical shells with various cross-sectional shapes are shown. In particular, for a shell of square cross section, the moment at the bifurcation is much lower than the maximum value; however, the initial post-buckling analysis reveals that the state of equilibrium is still stable. Deep post-buckling analysis is required to determine the moment carrying capacity of a shell with such cross section.     

Optimal design of axially symmetrical shells under hydrostatic pressure with respect to their stability

In this paper, the problem of optimal design of axially symmetrical shells against instability is considered. We look for the shape of middle surface as well as the thickness (constant or variable) of a shell, which ensure maximal value of the critical hydrostatic pressure. As the equality constraints the volume of material and the capacity of a shell are considered. The concept of a shell of uniform stability is applied. Received November 23, 1998     

Optimization of shell buckling incorporating Karhunen-Loève-based geometrical imperfections

The optimization of shell buckling is performed considering peak normal force and absorbed internal energy in the presence of geometrical imperfections implemented through Karhunen-Loève expansions. Initially, the mass of a shell is minimized in the presence of random initial imperfections by allowing cutouts in the material, subject to constraints on the average peak force and average internal energy. Then, robustness is considered by minimizing the coefficient of variation of the normal peak force while constraining the average peak force and average internal energy. LS-OPT® is used both to generate an experimental design and to perform a Monte Carlo simulation (96 runs) using LS-DYNA® at each of the experimental design points. The effect of imperfections when minimizing the mass is not large, but when considering robustness, however, the optimal design has a substantially increased hole size and increased shell thickness, resulting in a heavier design with maximal robustness within the constraints.     

Interfering effects of the task demands of grip force and mental processing on isometric shoulder strength and muscle activity

The purpose of this study was to examine the interfering effects of physical and mental tasks on shoulder isometric strength in different postures. Fifteen volunteers (seven women, eight men) performed a series of isometric shoulder exertions at 30°, 60° and 90° of both shoulder flexion and abduction alone and with the addition of a 30% grip force, a mental task (Stroop test) and both additional tasks simultaneously. The shoulder tasks were completed either at maximal intensity, or while maintaining a shoulder posture without any additional effort. Surface electromyography (EMG) from seven muscles of the shoulder girdle and shoulder moment were collected for each 6 s shoulder exertion. When normalized to maximum exertion, no differences were found between genders and no differences existed between conditions when subjects maintained each posture without exerted force. In the maximal shoulder exertion trials, an increase in shoulder angle (in either plane) resulted in an increase in EMG in most muscles, while shoulder moment decreased in flexion and remained constant in abduction. Shoulder moments and muscle activation were greatest in the shoulder exertion alone condition followed by adding a 30% grip and the Stroop test, with the addition of both tasks further reducing the exerted shoulder moment and EMG. However, muscle activity did not always decrease with shoulder strength and remained elevated, indicating a complex coactivation pattern produced by an interfering role of the tasks. Overall, it was found that a mental task can have the same or greater effect as a concurrent grip and should be considered when assessing muscular loading in the workplace, as typical biomechanical modelling may underestimate internal loads. The results not only provide valuable shoulder strength data but also practical strength values, depending on additional tasks.     

Computation of shape and drag of a deforming elastic body under fluid dynamic force

This paper describes numerical simulations for the shape and its drag of an elastic body deforming under the fluid dynamic force. The simulations were carried out by coupling the Navier-Stokes equations and the equations of motion of the elastic body. The equations of motion are formulated for an elastic shell model which is composed of material particles connected with elastic springs and dampers. The relation between deforming elastic body shape in response to the fluid dynamic force and its drag force was investigated under the constraint of constant volume and fixed center of gravity of the elastic body for incompressible and compressible supersonic flows. In these simulations, an initial shape of the elastic body is a circular cylinder and starts deformation under the fluid dynamic force.     

Interfering effects of the task demands of grip force and mental processing on isometric shoulder strength and muscle activity

The purpose of this study was to examine the interfering effects of physical and mental tasks on shoulder isometric strength in different postures. Fifteen volunteers (seven women, eight men) performed a series of isometric shoulder exertions at 30 degrees , 60 degrees and 90 degrees of both shoulder flexion and abduction alone and with the addition of a 30% grip force, a mental task (Stroop test) and both additional tasks simultaneously. The shoulder tasks were completed either at maximal intensity, or while maintaining a shoulder posture without any additional effort. Surface electromyography (EMG) from seven muscles of the shoulder girdle and shoulder moment were collected for each 6 s shoulder exertion. When normalized to maximum exertion, no differences were found between genders and no differences existed between conditions when subjects maintained each posture without exerted force. In the maximal shoulder exertion trials, an increase in shoulder angle (in either plane) resulted in an increase in EMG in most muscles, while shoulder moment decreased in flexion and remained constant in abduction. Shoulder moments and muscle activation were greatest in the shoulder exertion alone condition followed by adding a 30% grip and the Stroop test, with the addition of both tasks further reducing the exerted shoulder moment and EMG. However, muscle activity did not always decrease with shoulder strength and remained elevated, indicating a complex coactivation pattern produced by an interfering role of the tasks. Overall, it was found that a mental task can have the same or greater effect as a concurrent grip and should be considered when assessing muscular loading in the workplace, as typical biomechanical modelling may underestimate internal loads. The results not only provide valuable shoulder strength data but also practical strength values, depending on additional tasks.     

Limiting performance analysis of the protection of the human head from impact-induced injuries taking into account the duration of the shock pulse

The limiting possibilities of the protection of the human head from impacts by means of helmets are analyzed. The shell (base) of the helmet is assumed to decelerate after an impact against an obstacle with constant acceleration during a given time interval. The minimum of the peak magnitude of the displacement of the head (the object to be protected) relative to the helmet shell is determined, provided that the injury risk index does not exceed a prescribed tolerable value, as well as the corresponding time history of the absolute acceleration of the head. The injury risk index is defined by the HIC functional. This functional is adopted as a standard measure for the head injury risk in crash tests of vehicles, as well as in the tests of shock protection equipment for industries and sports. The time history of the motion of the head and the peak magnitude of the displacement of the head relative to the helmet shell are studied as functions of the shock pulse duration (the deceleration time of the helmet shell). The case of the instantaneous shock, when the shell comes to an instantaneous stop after hitting the obstacle, was considered in [1].     

Optimization of plastic spherical shells of von Mises material

An optimization procedure is developed for spherical shells pierced with a central hole. The outer edge of the shell is simply supported whereas the inner edge is absolutely free. The material of the shell is assumed to be an ideal plastic material obeying the von Mises yield condition. Resorting to the lower bound theorem of limit analysis, shells with constant and piece-wise constant thickness are considered. The designs of spherical shells corresponding to maximal load carrying capacity are established for a given weight. Necessary optimality conditions are derived with the aid of variational methods from the theory of optimal control. The obtained set of equations is solved numerically.     

一种被动力反馈阻尼器及其模型研究

根据力觉反馈的需要,设计了一种基于磁流变液的阻尼器,并建立了模型。介绍了磁流变液阻尼器的设计方法,该阻尼器由上、下盖组成密闭的壳体,转子通过轴设置于壳体内,壳体内充满磁流变液,在磁场作用下磁流变液屈服应力产生变化,转子相对于壳体转动时阻尼力连续快速变化,分析了阻尼器阻尼力构成及其可控性,运用较为简化的方法建立了阻尼器的逆动态模型,利用研制的阻尼器原型设计了实验系统并进行了挤压柔顺性物体和碰撞刚体力反馈实验,实验中阻尼器能够实现大范围的力觉反馈,因此表明设计方法有效、模型正确。     

车-简支梁桥耦合振动系统中全局最大动力响应研究

本文采用四分之一车辆模型和等截面简支梁模型,建立了车-桥耦合振动计算模型,分析了车辆匀速驶过桥梁时,桥梁动挠度、动弯矩、动剪力的全局最大值及发生的位置.进一步分析计算了车速、车距和桥梁模态截断阶数对桥梁动挠度、动弯矩、动剪力全局最大值的影响.结果表明,车速对桥梁动挠度、动弯矩、动剪力全局最大值影响较大,全局最大动挠度和全局最大动弯矩均出现在跨中附近,车速不同位置也不同,而全局最大动剪力均出现在车辆下桥的梁端;两车同时上桥时,前后车车距越大,桥梁动挠度、动弯矩、动剪力全局最大值越小,当达到一定车距时,三者不再减小且与单车情况相同;为提高桥梁动挠度、动弯矩、动剪力全局最大值计算精度,桥梁模态截断阶数宜分别大于3阶、6阶、7阶.     

Optimization of plastic conical shells of piece-wise constant thickness

Thin-walled conical shells subjected to uniformly distributed external pressure loading are considered assuming that the thickness of the shells is piece-wise constant. Minimum weight designs are established under the condition that the load carrying capacity of the optimized shell coincides with that of the reference shell of constant thickness. The material of the shell is assumed to obey Tresca's yield condition and the associated flow law. The exact yield surface in the space of generalized stresses corresponding to the Tresca condition is approximated with the squares on the planes of membrane forces and moments, respectively.     

On the capacity of the isoparametric quadratic beam element to solve accurately a uniformly loaded beam segment

It is well known that a quadratic isoparametric beam element integrated with two Gauss points solves exactly a beam segment with linearly varying moment and constant transverse shear force. Although widely used in practice, it seems to have passed unnoticed that the same element solves also exactly a beam segment with a parabolic moment and linear transverse shear. The paper fills this gap and presents a physical argument to show that the computed values of moment and shear match the actual values at the two Gauss points of the two point integration rule.     

Failure analysis of laminated composite cylindrical/spherical shell panels subjected to low-velocity impact

A 4-noded, 48 d.o.f. doubly curved quadrilateral shell finite element based on Kirchhoff–Love shell theory, is used in the nonlinear finite element analysis to predict the damage of laminated composite cylindrical/spherical shell panels subjected to low-velocity impact. The large displacement stiffness matrix is formed using Green's strain tensor based on total Lagrangian approach. An incremental/iterative scheme is used for solving resulting nonlinear algebraic equations by Newton–Raphson method. The damage analysis is performed by applying Tsai–Wu quadratic failure criterion at all Gauss points and the mode of failure is identified using maximum stress criteria. The modes of failure considered are fiber breakage and matrix cracking. The progressive failure analysis is carried out by degrading the stiffness of the material suitably at all failed Gauss points. The load due to low-velocity impact is treated as an equivalent quasi-static load and Hertzian law of contact is used for finding the maximum contact force. After evaluating the nonlinear finite element analysis thoroughly for typical problems, damage analysis was carried out for cross-ply and quasi-isotropic cylindrical/spherical shell panels.     

Non-linear strain-displacement equations exactly representing large rigid-body motions. Part III. Analysis of TM shells with constraints

The precise representation of arbitrarily large rigid-body motions in the displacement patterns of curved Timoshenko-Mindlin-type (TM) shell elements has been considered in Part I of the present work. In Part II it has been developed an enhanced mixed finite element formulation that allows using load increments that are much larger than possible with existing geometrically exact displacement-based shell element formulations. In this paper the developed formulation is employed to solve frictionless contact problems for TM shells undergoing finite deformations and interacting with rigid bodies. The contact conditions are incorporated into the assumed stress-strain TM shell formulation by applying a perturbed Lagrangian procedure with the fundamental unknowns consisting of 6 displacements and 11 strains of the bottom and top surfaces of the shell, 11 conjugate stress resultants and the Lagrange multiplier, associated with a nodal contact force, through using the non-conventional technique. The efficiency and accuracy of the proposed finite element formulation are demonstrated by means of several numerical examples.     

On the characteristics of optimum beams with optimum length surrounded by a Winkler’s medium

In this paper an analytical approach is used to optimize a beam surrounded by a Winkler’s medium and laterally loaded by a force at the top. The optimization regards both the distribution of the mass along the beam and the beam length in order to minimize the top displacement. Therefore, after having defined a transversality condition, we implement an algorithm to optimize the length of optimum beams. After having achieved the dimensionless extremals of optimum beams with optimum length, we show that the found solutions describe a central field of moment extremals defined along the beam and with the origin at the top. Having achieved the Jacobi’s condition and the strengthened Legendre’s condition for an extremal of optimum beam length, a sufficient condition for a weak minimum along the beam is also achieved. Besides, a given set of cross-sections whose moment of inertia divided by a dimensioned constant is obtained by raising their area to the same exponent. The optimized distribution of the dimensionless cross-sectional area as well as the dimensionless rigidity of the Winkler’s medium are intrinsic properties of all optimum beams with optimum length whose cross-sections belong to the same set.     

A biomechanical analysis of hip compression loading during lifting

The aims of the present study were (i) to calculate the magnitude and direction of the hip joint compressive force, (ii) to determine the influence of hip flexion angle on the compressive force and (iii) to design a diagram for easy predictions of hip extensor muscular forces.

A biomechanical analysis was performed using data from dissection, combined with data from our previous investigations into hip load moments during lifting, and into length of hip extensor muscular moment arms. Waters' load-sharing data were also included in the biomechanical model.

The compressive force during lifting a 126 N ( 12.8 kg) box in the sagittal plane with flexed and with straight knees was calculated to be between 2.6 and 3.2 times body weight and the force was found to be directed medially and slightly dorsally. At a constant hip joint loading moment, the degree of hip flexion greatly influenced the compressive force, the least force being obtained at 35° hip flexion. The use of the force prediction diagram developed is described. This diagram is proposed for practical use when assessing different work postures.     

Isokinetic strength aspects in human joints and muscles

The isokinetic concept of exercise has become an increasingly popular means to assess musculoskeletal function. The isokinetic apparatus enables the control of angular velocity of the moving limb (which is held constant during the range of movement) whilst giving an accomodated resistance. The resistance produced by the device is accommodated to the net external moment exerted by the subject. Some of the advantages of isokinetic assessment are discussed. However, a number of restrictions and limitations should be considered when interpreting these strength measurements.     

基于模糊人工势场法的智能全向车路径规划

针对于移动机器人在传统人工势场法路径规划中易于陷入局部最小点而无法抵达目标点的问题,同时考虑到实际环境中人工势场法相关参数的不确定性,提出了一种基于模糊人工势场法的动态路径规划方法。借助于专家经验进行模糊决策,调整移动机器人在各个时刻的合力大小和方向,进而解决斥力常数、引力方向偏角以及机器人行驶速度的不确定性问题。为了验证该方法的有效性,在智能全向车平台进行了应用,结果表明,智能全向车运动轨迹平滑,避免了实际应用中的震荡问题。