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Variational Principles and the patch test Fraeijs de veubeke, Baudouin in International Journal for Numerical Methods in Engineering (1974), 8 The patch test is shown to be contained in the variational formulations of the finite element methods at the assembling level, all of which require the vanishing of the virtual work of interface connexion ... [more ▼] The patch test is shown to be contained in the variational formulations of the finite element methods at the assembling level, all of which require the vanishing of the virtual work of interface connexion loads. By a systematic introduction of stress generating functions, attention is drawn to the fact that any given finite element model can be assembled in two different ways: either by identiification of a set of boundary displacements (leading to the direct stiffness method), or by identification of a set of local stress function values (leading to the dual direct flexibility method). Looking at any conjugate couple (generalized displacement - generalized surface traction) at an interface, one is strongly transmitted, the other weakly. Discretization of the zero virtual work condition at an interface of plate bending models, by means of Legendre polynomials expansions, allows q systematic construction of so-called "non-conforming" elements that pass the patch test. They are in fact identified with weakly conforming, but strongly diffusive , htbrids, and the lowest degree element (quadratic) is in fact the Morley constant-moment element. Examples are given for higher displacement fields. The case of plate stretching elements can be handles by duality, the difficulties being here associated with the requirements for diffusivity. Non diffusive elements that pass the zero interface virtual worktest can be constructed systematically and are identifiable with weakly diffusive, but strongly conforming, hybrids, of the type first proposed by T.H.H. Pian. [less ▲] Detailed reference viewed: 78 (9 ULg)Diffusive equilibrium elements Fraeijs de veubeke, Baudouin Scientific conference (1973, July) Equiliobrium models are characterized by an internal stress field in equilibrium and surface tractions that should obey the diffusivity requirement of reciprocity with adjacent elements at the interfaces ... [more ▼] Equiliobrium models are characterized by an internal stress field in equilibrium and surface tractions that should obey the diffusivity requirement of reciprocity with adjacent elements at the interfaces. Thepaper discusses the construction of stiffness matices for such elements and the difficulties associated with the presence of mechanisms. The use of first order or second order stress functions is presented together with the possibility of solving the final equations by the force method through a direct flexibility method. Three methods are presented for getting rid of thre machanisms: the classical superelement technique, a method based on the discretization of rotational equilibrium and quasi-diffusivity. [less ▲] Detailed reference viewed: 31 (8 ULg)A new variational principle for finite elastic displacements Fraeijs de veubeke, Baudouin in International Journal for Engineering Science (1972), 10(9), 745-763 After a discussion of existing variational principles, a new set of variational principles, of displacement, canonical or complementary energy types, is found to derive from the polar decomposition of the ... [more ▼] After a discussion of existing variational principles, a new set of variational principles, of displacement, canonical or complementary energy types, is found to derive from the polar decomposition of the jacobian. It involves the engineering strain tensor and its conjugate stress tensor is to be regarded as a function of the Piola tensor and the material rotaion. The complementary energy formulation is discussed in terms of firs order stress functions. The presence of the rotational degrees of freedom opens the possibility of discretizing the rotational equilibrium equaions in approximate solutions. [less ▲] Detailed reference viewed: 88 (11 ULg)An equilibrium model for plate bending Fraeijs de veubeke, Baudouin ; in International Journal of Solids and Structures (1968), 4 A conforming displacement model for plate bending was presented earlier. It is of intyerest to have also an equilibrium moàdel available in order to generate both upper and lower bounds to plate ... [more ▼] A conforming displacement model for plate bending was presented earlier. It is of intyerest to have also an equilibrium moàdel available in order to generate both upper and lower bounds to plate deflections. The theory of the triangular equilibriium model, which is presented here, takes advantage of oblique coordinates. Il allows to cover transvers loading modes. Because the numerical investigations required adaptibility of the model to a stiffness computer-program, only the elaboration of the stiffness matrix was aimed at. The element can nevertheless be recognised as the Southwell analogue of the plane stress model with quadratic displacement field. As such it can be handled efficiently by a force program. Numerical results show the monotonic convergence of deflections from above for the equilibrium model and from below for the conforming model. The convergence rate, in terms of generalized coordinates, is compâred with that of other plate bending elements. [less ▲] Detailed reference viewed: 66 (9 ULg)A conforming finite element for plate bending Fraeijs de veubeke, Baudouin in International Journal for Solids ans Structures (1968), 4 In this paper, the celeber CQ (conforming quadrilateral) element of plate is presented for the first time. Detailed reference viewed: 117 (5 ULg)Variational principles in fluid mechanics Fraeijs de veubeke, Baudouin in 7e Conférence scientifique sur la Mé&canique des Fluides (1965) This paper attemps a completely logical derivation from Hamilton's principle to a purely eulerian principle. A logical step, which departs from the procedure adopted by Lin, has been taken. Since ... [more ▼] This paper attemps a completely logical derivation from Hamilton's principle to a purely eulerian principle. A logical step, which departs from the procedure adopted by Lin, has been taken. Since independent variations are to be taken on the velocity field, it is only natural to remove the constraints implying that the velocity is the derivative of the poarticle's position vector. This introduces a new vector multiplier enjoing a property of constant circulation along any segment fixed in the flow. This procedure yelds almost immediatly a general variational principle that can easily be specialized to the principles given by Bateman. [less ▲] Detailed reference viewed: 69 (5 ULg)Displacement and equilibrium models in the finite element method Fraeijs de veubeke, Baudouin in Zienkiewicz, O. C.; Holister, G. S. (Eds.) Stress Analysis (1965) A capital contribution to the finite element method, including for the first time equilibrium models, dual analysis, the quadratic displacement element, a discussion of mixed formilation, and the ... [more ▼] A capital contribution to the finite element method, including for the first time equilibrium models, dual analysis, the quadratic displacement element, a discussion of mixed formilation, and the limitation principle. [less ▲] Detailed reference viewed: 1503 (6 ULg)Sur certaines inégalités fondamentales et leur généralisation dans la théorie des bornes supérieures et inférieures en élasticité Fraeijs de Veubeke, Baudouin in Revue Universelle des Mines (1961) In this paper, the bases of the celebrated dual analysis are given for the first time. Detailed reference viewed: 48 (7 ULg)Difusion des inconnues hyperstatiques dans les voilures à longerons couplés Fraeijs de veubeke, Baudouin in Bulletin du Service Technique de l'Aéronautique (1951), 24 This paper contains a first set of applications of the variational principles of elasticity to aeronautical structures. Detailed reference viewed: 66 (33 ULg) |
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