摘要:

AbstractA finite element model is presented for the analysis of the thermal stress development in a body with temperature dependent material properties. The thermal model allows a change of phase to occur within the body and an elasto‐viscoplastic constitutive relationship is used for the stress analysis. An example is given of the applicability of the technique to the analysis of continuous casting in metal

ISSN:0029-5981    

DOI:10.1002/nme.1620140102

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractFinite element equivalents of the equations governing shearing and buoyancy driven flows are derived, and reduced to upwind forms suitable for the solution of problems in which the Reynolds and Rayleigh numbers are large. A modification to the central difference iterative method is studied which increases the Reynolds and Rayleigh numbers for which a central difference form may be used. A comparison is made between the results obtained using the central and upwind forms of the finite element method and those predicted by finite difference methods in the case of flow in a cavity. A mesh refinement study is made. The upwind forms of the finite element equations are applied to the solution of a complex flow problem involving the flow of glass in a throated furnace in the case of constant‐ and temperature‐ dependent viscosity and conductiv

ISSN:0029-5981    

DOI:10.1002/nme.1620140103

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620140104

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe 18 degree‐of‐freedom flat triangular shell element is reformulated by combining the well‐known bending triangle with a plane stress triangle incorporating in‐plane rotations at each vertex. Both elements are displacement formulated. The plane stress element's displacement interpolation isincompleteand hence convergence to exact solutions is precluded. Comprehensive test results are presented for several types of problem including plane stress, thin shells and folded plates. The results indicate that the element does produce rapidly convergent answers. However these answers are not the correct ones, although they may be acceptable engineering approximations in many applications. Further, the element seems to provide reasonably good results even for relatively coarse elemen

ISSN:0029-5981    

DOI:10.1002/nme.1620140105

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractA finite element analysis technique for an arbitrarily laminated anisotropic plate is described. A superparametric quadratic plate element with five degrees‐of‐freedom per node is used in the analysis. A stress‐strain relation is derived from a three‐dimensional approach to the problem. The volume integration of the stiffness matrix is evaluated by numerical integration using the Gauss quadrature formula with 2 × 2 × 2 sampling points. A variety of laminated plate problems is solved and the results are compared with the exact solutions, which demonstrate the validity of t

ISSN:0029-5981    

DOI:10.1002/nme.1620140106

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe paper considers the finite element analysis of the free, undamped and the forced damped vibrations of rotationally periodic structures. Associated with every natural frequency (except for those for which the deflection is the same at corresponding points on every substructure) there are a pair of orthogonal mode shapes, with eigenvectors {u} and {ü}. The complex vector {z}={u}+i{ü} is also an eigenvector of the equations of motion, and represents a rotating normal mode. The deflection of one substructure has the same amplitude as, and a constant phase difference from the deflection of the preceding substructure. It is therefore possible to analysse the complete structure by considering only one substructure, and applying appropriate complex constraints at its boundary with the following substructure, so as to and applying appropriate complex constrainsts at its boundary with the following substructure, so as to impose this phase difference. The method has been implemented in a computer program and is illustrated by analyses of an alternator end winding, a cooling tower with legs, and a wheel of turbine blades.For forced vibration, it is shown that any arbitrary oscillatory force can be decomposed into a series of rotating forces. For any one of these rotating components, there is a fixed relationship between the amplitude and phase of the force acting on one substructure, and that acting on an adjoining substructure. This relationship, which does not involve any approximation, can be used to enable a series of calculations of the response of one substructure to be performed instead of one on the whole structure. A series of calculations on an individual substructure normally requires much less computer time and storage than a single calculation on the complete structur

ISSN:0029-5981    

DOI:10.1002/nme.1620140107

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractA new finite element technique for two‐dimensional viscous incompressible fluid flow problems is presented in this paper. The vorticity transport equation is integrated in a small control volume, which results in the conservation law of vorticity. The finite element technique is applied to this equation together with the continuity equation, where simple linear triangular elements with three nodes are used for the formulation. Resulting sets of algebraic equations are solved by the use of a kind of relaxation method. Numerical results for viscous flow past a cavity show good agreement with experimental result

ISSN:0029-5981    

DOI:10.1002/nme.1620140108

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractLoad‐free notch surfaces of bodies made of a linear‐elastic, homogeneous, isotropic material are optimized within given variation domains by means of an interation procedure so that the occurring maximum tangéntial stress is reduced to a minimum. The hypothesis of a constant tangential stress distribution for obtaining minimal notch stresses proposed by R. V. Baud has been confirmed by means of the Fade‐away Law of the notch stress theory. The finite element method is applied for calculating the displacement and stress field of the styructure. An increment procedure is used for determing the displacement field after every iteration step, which permits the calculation of the displacement quantities with sufficient accuracy in a single step. Numerical solutions and their comparison with analytical solutions and stress results obtained with the aid of photo‐elasticity confirm the usefulness of this procedure. The known optimization methods1,2differ from those used in the prese

ISSN:0029-5981    

DOI:10.1002/nme.1620140109

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractAn implementation of the Ahmad Thick Shell element using vector manipulation, reduced integration and the incorporation of the missing term in the approximating polynomial is presented. The first two aspects are merely applications. The theory is presented elsewhere6,7,11,18and will not be repeated for the sake of conciseness. The third aspect was achieved by adding to the original nodal configuration a central node having only one degree‐of‐freedom. That node is then eliminated to preserve the original number of degrees‐of‐freedom.The Ahmad thick shell element is adequately presented in finite element literature.1‐3The co‐ordinate definition and the displacement field are retained and will not be dealt with henceforth. However, a different concept of the strain definition due to Irons is used and the bending terms are included in the modulus matrix.The element like all second generation isoparametric elements is easily implemented through a shape function subroutine suitable for quadrilaterals. It reproduces exactly rigid body motion for any combination of elements of any geometry even for elements withcurved sides and variable thickness. Although Ahmad's thick shell element passed the patch test for unequal parallelograms but not for quadrilaterals the version presented passes that test for quadrilaterals.In spite of its credentials, the new version denoted by A has a major setback. the presence of one too many spurious mechanism

ISSN:0029-5981    

DOI:10.1002/nme.1620140110

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractA method by which the numerical difficulties that one encounters while attempting to solve the differential equations which describe a diffusion flame can be circumvented is the quasi‐linearization technique. Application of this method in conjunction with difference approximations transforms the equations into tri‐diagonal matrices which can be inverted by the Thomas method. Since this is an iterative method initial profiles are generated by employing Burke‐Schumann kinetics. This method is found to be superior to the marching techiques that are frequently used in the analyses of diffusion f

ISSN:0029-5981    

DOI:10.1002/nme.1620140111

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY