摘要:

AbstractThis is the first paper of a pair which together discuss the development of a class ofoverlapping hinged bending finite elementswhich are suitable for the analysis ofthin‐shell,plateandbeamstructures. These elements rely on a simple physical analogy, involving overlapping hinged facets. They are based onquadratic overlappingassumed displacement functions. Only translational nodal degrees of freedom are necessary, which is a significant simplification over most other currently available beam, plate and shell finite elements which employ translational, rotational and higher‐order nodal variables. In this paper the hinged bending element concept is introduced, and thehinged beam bending(HBB) andhinged plate bending(HPB) elements are formulated. In paper II these concepts are extended to develop ahinged shell bending(HSB) element. The HSB element can be readily combined with theconstant strain triangular(CST) plane stress finite element for the modelling of thin‐shell struc

ISSN:0029-5981    

DOI:10.1002/nme.1620350502

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThis paper is the second of a pair which discuss the development of a class ofoverlapping hinged bending finite elements, which are suitable for the analysis ofthin‐shell,plateandbeamstructures. These elements rely on a simple physically appealing analogy, in which overlapping hinged facets are used to represent bending effects. They are based on quadraticoverlappingassumed displacement functions, which results in constant stress/strain representation. Only translational nodal degrees of freedom are necessary, which is a significant advantage over most other currently available beam, plate and shell finite elements which employ translational, rotational and higher‐order nodal variables. In paper I the hinged bending element concept has been introduced, and thehinged beam bending(HBB) andhinged plate bending(HPB) elements formulated. In the present paper these concepts are extended to develop ahinged shell bending(HSB) element. The HSB element can be readily combined with theconstant strain triangular(CST) plane stress finite element for the modelling of thin‐shell structures; and the combined HSB‐CST element is tested against a number of 'standard' thin‐shell problems. The present paper, like paper I, is conducted entirely in the context of small‐displacement elasti

ISSN:0029-5981    

DOI:10.1002/nme.1620350503

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA simple 4‐node assumed‐stress hybrid quadrilateral shell element with rotational or 'drilling' degrees of freedom is formulated. The element formulation is based directly on a 4‐node element. This direct formulation requires fewer computations than a similar element that is derived from an 'internal' 8‐node isoparametric element in which the midside degrees of freedom are eliminated by expressing them in terms of displacements and rotations at corner nodes. The formulation is based on the principle of minimum complementary energy. The membrane part of the element has 12 degrees of freedom, including the drilling degrees of freedom. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner‐Mindlin plate theory which takes into account the transverse shear effects. Quadratic variations for both in‐plane and out‐of‐plane displacement fields and linear variations for both in‐plane and out‐of‐plane rotation fields are assumed along the edges of the element. The element Cartesian‐co‐ordinate system is selected such as to make the stress field invariant with respect to node numbering. The membrane part of the stress field is based on a 9‐parameter equilibrating stress field, while the bending part is based on a 13‐parameter equilibrating stress field. The element passes the patch test, is nearly insensitive to mesh distortion, alleviates the 'locking' phenomenon, is invariant with respect to node numbering, has no hidden spurious modes, and produces

ISSN:0029-5981    

DOI:10.1002/nme.1620350504

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe paper is concerned with first order approximation methods to solve non‐linear optimization problems as they arise in structural optimization. A modification of the original Method of Moving Asymptotes (MMA) is presented to prevent oscillation or divergence by incorporating a line‐search into the global iteration algorithm. In this line‐search a merit‐function of augmented Lagrangian type is decreased by using a backtracking strategy. A proof is presented to show the descent property of the proposed merit‐function for MMA. Numerical examples demonstrate how the new technique stabilizes the iteratio

ISSN:0029-5981    

DOI:10.1002/nme.1620350505

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe finite element implementation of a lamina‐based elastic constitutive relation appropriate for describing the three‐dimensional (3‐D) behaviour of fibre composite laminated media is presented. Unconstrained by the two‐dimensional restrictions accompanying plate and shell theories, this approach resolves the macro 3‐D deformation fields found in 'thick' laminated or filament wound composites without requiring each lamina to be individually discretized to assign material properties. In rectangular isoparametric solid elements where laminae locally parallel an element 'face', the implementation represents 'exactly' the elastic laminate behaviour by replacing the discrete lamina stiffnesses with continuous polynomial moduli functions. Attributable directly to thelaminaconstitutive relationship used, appropriate for fibre‐dominated material systems, the implementation automatically preserves interlaminar continuity of tractions and displacements within each element for laminates assembled from a single lamina type. The order of the effective moduli functions is determined by the element kinematics and by requiring identical net mid‐surface elemental forces and moments. In general, this representation substantially reduces the number of stored variables and through‐thickness integrations required, and allows 'exact' integration by higher‐order Gaussian quadrature. Additionally a single element may span any portion or number of laminae, thus allowing nearly arbitrary meshing and solution resolution. Several numerical examples using 3‐D 8‐node isoparametric solid elements demonstrate the approach's convergence

ISSN:0029-5981    

DOI:10.1002/nme.1620350506

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe problem of cathode shape determination for a given anode shape in electrochemical machining is considered. An algorithm based on the boundary integral equation technique and non‐linear optimization for this inverse problem is developed. The additional flux condition at the anode is used as the constraint in this ill‐posed problem. Through an iterative process, the shape of the cathode is determined by minimizing a functional. The algorithm is tested on two examples. It is shown that the algorithm is consistently superior compared to published numerical techniques based on the embedding method or the method of the li

ISSN:0029-5981    

DOI:10.1002/nme.1620350507

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractOptimum engineering design problems are usually formulated as non‐convex optimization problems of continuous variables. Because of the absence of convexity structure, they can have multiple minima, and global optimization becomes difficult. Traditional methods of optimization, such as penalty methods, can often be trapped at a local optimum. The tabu search method with random moves to solve approximately these problems is introduced. Its reliability and efficiency are examined with the help of standard test functions. By the analysis of the implementations, it is seen that this method is easy to use, and no derivative information is necessary. It outperforms the random search method and composite genetic algorithm. In particular, it is applied to minimum weight design examples of a three‐bar truss, coil springs, a Z‐section and a channel section. For the channel section, the optimal design using the tabu search method with random moves saved 26.14 per cent over the weight of the SUMT m

ISSN:0029-5981    

DOI:10.1002/nme.1620350508

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA novel method is presented in this paper for calculating shape design sensitivity, which is based on the finite difference method (FDM). By analysing the numerical procedure of the FDM, the perturbation of the geometry is replaced by a perturbation load which can be calculated once the stress field of the initial problem and the design boundary perturbation are known. The final shape design sensitivity is obtained by solving the perturbation problem which has the same geometry and the kinematical boundary condition as the initial problem, but under the perturbation loads. Therefore the new method does not require the calculation of the matrices of the perturbed structure, and is independent of the perturbation step. A numerical implementation of the finite difference load method (FDLM) is described in which the boundary element method is used to evaluate the structural response. The numerical examples demonstrate that this new method for shape design sensitivity analysis is very accurate.

ISSN:0029-5981    

DOI:10.1002/nme.1620350509

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe finite strip method is developed for predicting the geometrically non‐linear response of rectangular composite laminates with simply supported ends when subjected to uniform end shortening in their plane. At the loaded ends lateral in‐plane expansion may be allowed freely or may be prevented completely in different versions of the approach. The permitted laminate material properties are quite general, encompassing anisotropy and full coupling between in‐plane and out‐of‐plane behaviour. The analysis is based on the use of the classical plate theory and the non‐linearity is introduced in the strain‐displacement equations in the manner of the von Karman assumptions. Three different types of finite strip are presented with either linear, quadratic or cubic interpolation of the membrane displacement components across a strip: in each case the bending displacement component varies cubically across a strip. Results are presented for isotropic plates and for unsymmetric cross‐ply, angle‐ply and ar

ISSN:0029-5981    

DOI:10.1002/nme.1620350510

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA theory of rubberlike membrane shells undergoing large elastic deformations is derived. The stresses are deduced from Ogden's material law, which is formulated in terms of the principal values of the right stretch tensor. Incompressibility is fulfilled exactly using the plane stress constraint. Furthermore, a finite element formulation of the membrane theory is given. The use of the tangential stiffness matrix, derived analytically, provides a quadratically convergent solution process. Several numerical examples show the robustness of the developed finite element.

ISSN:0029-5981    

DOI:10.1002/nme.1620350511

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY