SUMMARYThe present paper describes a procedure for the optimal dimensional synthesis of mechanisms which is based on the solution of non-linear position problems. Planar mechanisms are modelled very easily by means of finite elements of bi-hinged rod type. The judicious choice of constraint conditions makes possible the solution of classical position problems: initial, finite-displacement, deformed and static-equilibrium problems, as well as the main types of dimensional synthesis: path generation, functions, rigid body guidance, mixed, and multiple. A single synthesis error function applies to all these types, and moreover is general since it is valid for mechanisms of any configuration. This function is based on the idea that the best mechanism for the given synthesis conditions is the one that least needs to be deformed when it is obliged to satisfy them exactly, to which end the elastic deformation of the elements is permitted.1997 by John Wiley & Sons, Ltd.

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Zhu [20,21] adopt, as a true stress field, an enhanced field that in conjunction with the field deriving from the FE solution defines the energy norm for error displacements. The procedure of adopting as a true field an enhanced or smoothed field on the basis of the field obtained via FEs has become well established [22,23].The foregoing references are mainly to material dealing with linear static problems. However, in recent years there has been a dramatic increase in the number of specific estimators for dynamics [24,25], for non-linear geometric problems [26], for plasticity [27], for problems of contact with friction[28], for numerical simulation of forming processes [29] and more. At the same time the validation of estimators is becoming more rigorous. It is not enough simply to compare with simple models of known theoretical response, or with reference models having a high number of degrees of freedom. Systematic methodologies [30] are appearing whose purpose is to assess the quality of any given estimator.As regards the other base for adaptive meshing, i.e. the enrichment of the mesh, there are various alternatives. Perhaps the oldest is the recollocation of the degrees of freedom over the domain [31]. This procedure, sometimes referred to as r-line, is mainly used when the geometric irregularity of the elements making up the mesh is large, and as a basis for other alternatives. Its main difficulties are two: the resulting system of equations is non-linear, and the restricting conditions over the boundary will at times resist analytic expression. The two following alternatives are the h-line and p-line, which are the more lavishly developed [32]. The hierarchical concept [33] can be introduced into the h-line or into the p-line, the latter option being the easier. While on first inspection this concept appears to offer fine advantages, its complexity and the difficulty entailed in coupling it to commercial programs have hindered its popularity. Finally there is the hp-refinement, the capacity of which has been demonstrated in a lot of recent and interesting work [34][35][36]. But the complexity of the procedure continues, and its efficacy for practical purposes is not high enough. Hence today there still do not exist commercial FE programs using the hp-refinement in pure form. What we do indeed find are simplified procedures for a combined use of h and p-refinements [37].It remains to point out that FE packages require a particular organization and a database suitable for the construction of adaptive meshes [38,39]. The success of some estimators and of some refinement or remeshing procedures is a consequence of the ease with which they can be included in the organizational structure of an already existing FE program. The present paper describes an automatic scheme of adaptive meshing in which error assessment is based on the SED and the mesh enrichment involves a simplified hp-refinement procedure.Basis for a refinement procedure The procedure discussed here applies basically to elastostatic two-dimension...

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