摘要:

AbstractThis paper presents an investigation of using orthogonal constant and higher order stress modes in formulating efficient hybrid elements by equipping the primary idea of Bergan and Hanssen. Two sample elements modified from Pian‐Sumihara 5‐β plane and Pian‐Tong 18‐β hexahedral assumed contravariant stress elements are derived. With the suggested admissible simplifications of the flexibility matrices incorporated into the two new elements, new plane and hexahédral elements requiring respectively no and a negligible amount of computing efforts for inverting the flexibility matrices are formed. All, proposed elements are stable, invariant, contain no empirically determined factor and strictly pass the patch test. Popular benchmark problems are studied and the accuracy of the proposed elements is close to their par

ISSN:0029-5981    

DOI:10.1002/nme.1620350102

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe algorithm optimization presented uses the optimality criteria method so as to minimize the total weight of the structure in the presence of a constraint of the damping type. The goal of this study is to increase the structural damping by optimizing the viscoelastic and elastic material distribution over the structure. The types of damping considered are hysteristic. The gradient of the constraint function in relation to the design variables is calculated with the aid of a complex variable sensitivity method. Several numerical results are presented to validate the algorithm proposed.

ISSN:0029-5981    

DOI:10.1002/nme.1620350103

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA non‐linear 9‐node stress resultant shell finite element with six degrees of freedom per node is formulated. The material non‐linearity is based on an implicit integration scheme using the von Mises yield criterion and linear isotropic bardening. The small strain geometric non‐linearity is formulated using the polar decomposition theorem of continuum mechanics via a corotational updated Lagrangian method, which represents finite rotations with accuracy. Reduced integration is used to remove locking and calculate the stresses at their optimal stress accuracy points. A practical procedure is employed to stabilize the troublesome spurious zero energy modes. A number of tests covering the non‐linear material and geometry ranges and buckling show the good performance of the ne

ISSN:0029-5981    

DOI:10.1002/nme.1620350104

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA general theoretical framework is presented for the fully non‐linear analysis of shells by the finite element method. The governing equations are derived exclusively in terms of resulting quantities through a logical and straightforward descent from three‐dimensional continuum mechanics without appealing to simplifying assumptions (hence the name genuinely resultant). As a result, the underlying theory is statically and geometrically exact, and it naturally includes small strain and finite strain problems of thin as well as thick shells. The underlying mathematical structure and the variational formulation of the theory are examined. This appears to be crucial for the development of computational procedures employing the Newton‐Kantorovich linearization process and the Galerkin type discretization method. The treatment of finite rotations through an arbitrary parametrization of the rotation group and the interpolation procedure of SO(3)‐valued functions underlying the construction of finite element basis are other issues studied in this paper. A numerical analysis is presented in order to assess the effectiveness of the proposed formulation. Small strain problems as well as finite strain deformation of rubber‐like shells undergoing finite rotations are considered. Special attention is devoted to the assessment of the relevance of the drilling degree‐of‐freedom and highly non‐uniform through‐the‐thickness deformation in the case of shells made of inco

ISSN:0029-5981    

DOI:10.1002/nme.1620350105

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractShape functions and numerical integration formulas for three‐dimensional finite element analysis as found in most finite element reference books are incomplete. For example, shape functions and integration formulas for a pyramid with a quadrilateral base are missing. It is also difficult to find symmetric higher‐order integration formulas for triangular and tetrahedral elements. In general, these shape functions and integration formulas cannot be satisfactorily derived as degenerate cases of shape functions and integration formulas for hexahedral (brick) elements. In this paper we presentC°‐continuous quadrilateral pyramid elements and integration formulas for two‐ and three‐dimensiona

ISSN:0029-5981    

DOI:10.1002/nme.1620350106

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA novel technique is developed to simulate the effects of an infinite elastic solid by using multiple springs having spatially varying stiffnesses. The spring constants are computed by numerical integration of classical solutions for point or line loads in an infinite or semi‐infinite elastic mass. Under certain conditions, even the 'exact' values of spring constants may become negative at some nodes. A simple and highly effective algorithm is proposed to remove this computational difficulty. The technique is applied to the computation of displacements and stresses around underground openings. For a circular opening subjected to different stress conditions, spring constants computed by the proposed numerical integration technique are found to be 'identical' to their 'exact' values. Results obtained by the proposed technique for displacements and stresses around circular and non‐circular openings are found to be in an excellent agreement with classical and boundary element solutions. The principal advantages of the proposed technique are that an unbounded solid may be simulated by a relatively very small finite model and a standard finite element code requires no modification for its implementat

ISSN:0029-5981    

DOI:10.1002/nme.1620350107

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA simple and reliable method of aerodynamic design of airfoils is proposed for a given range of the angle of attack. The method is based on the solution of a new inverse boundary‐value problem of aerohydrodynamics. In the problem the initial velocity distributions are given along the contour of the required airfoil as a function of the are co‐ordinate for extreme values of the angle of attack from a fixed range. We justify a method of choice of these distributions which guarantees a non‐stalling flow around the airfoil. The problem of airfoil optimization is also considered. Results of numerical calculations are pres

ISSN:0029-5981    

DOI:10.1002/nme.1620350108

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA finite element formulation for the large sliding contact problem is discussed. With respect to a set of two material points the free and contacting state are distinguished. Because of the possibly occurring large slidings, the two points contact conditions are transformed to contact conditions with respect to larger sets of points, the so‐called contact units. An incremental solution strategy is presented which calculates the equilibrium solution that obeys these contact conditions using an iterative procedure. Part of this strategy is the identification of actual sets of contacting material points. The performance of the algorithm is demonstrated by some case‐stud

ISSN:0029-5981    

DOI:10.1002/nme.1620350109

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractAn adaptiveh‐refinement procedure utilizing compatible 5‐ to 7‐node quadrilateral transition elements together with 4‐node elements is presented for Reissner–Mindlin plate bending problems. By introducing the transition elements which have physical midside nodes, some difficulties associated with imposing displacement constraints on irregular nodes to enforce interelement compatibility in common adaptiveh‐refinement on quadrilateral mesh are easily overcome. Numerical examples are presented to show the effectiveness of using the transition elements for the adaptiveh

ISSN:0029-5981    

DOI:10.1002/nme.1620350110

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractDiscrete source superposition techniques seek sets of discrete, singular source strengths which satisfy the boundary conditions of a particular problem, and, necessarily, the governing differential equation. The sum of the fields produced by such sources thus provides an approximation to the required solution. In many respects these techniques are a special case of conventional boundary integral equation methods, where density distributions of smeared sources are sought. In this paper an attempt is made to extend the discrete source superposition technique to transient problems. The example addressed is the transient diffusion equation. The method developed does seem to have sòme promise. It is found that even coarse spatial discretization can yield quite accurate results, and that surprisingly large timesteps can be employed and accuracy maintained. Further, although no direct comparisons are made, the absence of spatial integrations indicates that the computational effort per timestep is likely to be less than for conventional BIE

ISSN:0029-5981    

DOI:10.1002/nme.1620350111

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY