1,720,992 research outputs found
On the adjoint constitutive law in nonlinear elastic optimal design
No full textThis work is concerned with a structural optimization problem, formulated in quite general terms, involving an elastic nonlinear isotropic three-dimensional continuum. The resolution is approached through a variational technique (Lagrange multiplier method); this technique yields, in addition to the optimality condition, a set of equations which can be interpreted as governing equations of another structural problem, “adjoint” to the given one. The constitutive law of the adjoint problem is studied in detail and the differences between the real and the adjoint constitutive laws are pointed out. In particular, it is shown that the material of the adjoint problem is orthotropic and its principal directions of orthotropy are determined. Finally. the results obtained are specialized to a «compliance» optimization problem for elastic nonlinear plates in bending; the difference between the present case and the already known case where the plate is linearly elastic is discussed
Bounds on the elastic strain energy density in 3-D bodies with material symmetries
No full textDealt with is the determination of the orientation of the material symmetry axes at which a 3D body made of aleotropic materials exhibits the stiffest (or possibly, the most flexible) response. As a general rule, this is shown to require co1linearity of principal stresses and principal strains. The two cases of materials with cubic symmetry and transversely isotropic materials are studied in detail. For transversely isotropic materials, optimal solutions can be either ‘trivial’, i.e. featured by full col1inearity of material symmetry axes and principal strains. or ‘quasi-trivial’, where collinearity is only partial1y preserved. For materials with cubic symmetry. possible are also ‘non-trivial’ solutions. featured by equal axial strains along the three symmetry axes. Optimal orientations are analytically derived and the relevant solutions classified: of great importance to this end is a parameter depending only on the elastic material properties
Estremi dell’energia di deformazione per solidi elastici trasversalmente isotropi
No full textDealt with is the determination of the orientation of the material symmetry axes at which a 3D body made of aleotropic materials exhibits the stiffest (or possibly, the most flexible) response. As a general rule, this is shown to require co1linearity of principal stresses and principal strains. The two cases of materials with cubic symmetry and transversely isotropic materials are studied in detail. For transversely isotropic materials, optimal solutions can be either ‘trivial’, i.e. featured by full col1inearity of material symmetry axes and principal strains. or ‘quasi-trivial’, where collinearity is only partial1y preserved. For materials with cubic symmetry. possible are also ‘non-trivial’ solutions. featured by equal axial strains along the three symmetry axes. Optimal orientations are analytically derived and the relevant solutions classified: of great importance to this end is a parameter depending only on the elastic material properties
Estremi dell'energia di deformazione per solidi anisotropi
No full textA general procedure for the explicit evaluation of all the critical points (hence, of absolute maxima and minima) of the strain energy density in anisotropic solids is shown. First, the general formulation is given irrespective of the symmetry class to which the solid belongs. Then, referring to the tetragonal, hexagonal and cubic symmetries, all the stationarity points are explicitly evaluated
On coaxiality of stress and strain fields and stationarity of elastic energy in anisotropic solids
No full textCoaxiality of the stress and strain tensors is a necessary condition for the stationarity of the strain energy density in linearly elastic anisotropic solids. This condition is exploited to explicitly evaluate the critical points of the energy, for a given state of strain, when a material element is rotated respect to the principal directions of strain. The complete solution, in terms of critical points and classification of the corresponding energy values, is given for solids endowed with cubic, hexagonal-5 and tetragonal-6 symmetry. Some preliminary results concerning the more general case of orthorhombic symmetry are also presented
Sensitivity analysis and optimum design of elastic-plastic structural systems
No full textThe paper deals with elastic-plastic optimization of flexural structural systems, subjected to kinematic restrictions. A finite holonomic piecewise linear elastic-hardening constitutive law is adopted. Sensitivity analysis for the displacement field is also performed, and a suitable finite element formulation, allowing for the spreading of plasticity, is also given. Finally, some meaningful numerical applications, together with their physical interpretation, are presented
Estremi del modulo di Young per alcune classi di anisotropia
No full textFor a homogeneous anisotropic linearly elastic solid, the general expression of Young’s
modulus E(n), embracing all classes that characterize the anisotropy, is given. A constrained extremum problem is then formulated for the evaluation of those directions n at which E(n) attains stationary values. Cubic and transversely isotropic symmetry classes
are dealt with, and explicit solutions for such directions n are provided. For each case,
relevant properties of these directions and corresponding values of the modulus are discussed as well. Results are shown in terms of suitable combinations of elements of the elastic tensor that embody the discrepancy from isotropy
Extrema of Young’s modulus for cubic and transversely isotropic solids
No full textFor a homogeneous anisotropic and linearly elastic solid, the general expression of Young's modulus E(n), embracing all classes that characterize the anisotropy, is given. A constrained extremum problem is then formulated for the evaluation of those directions n at which E(n) attains stationary values. Cubic and transversely isotropic symmetry classes are dealt with, and explicit solutions for such directions n are provided. For each case, relevant properties of these directions and corresponding values of the modulus are discussed as well. Results are shown in terms of suitable combinations of elements of the elastic tensor that embody the discrepancy from isotropy. On the basis of such material parameters, for cubic symmetry two classes of behavior can be distinguished and, in the case of transversely isotropic solids, the classes are found to be four. For both symmetries and for each class of behavior, some examples for real materials are shown and graphical representations of the dependence of Young's modulus on direction n are given as well
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