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**Structural mechanics - a unified approach.**
*(English)*
Zbl 0863.73004

London: E & FN Spon/ an impr. of Chapman & Hall. xv, 761 p. (1997).

This text intends to provide a complete and uniform treatment of the fundamental themes of structural mechanics, ranging from the more traditional to the most advanced.

The mechanics of linear elastic solids (beams, plates, shells, three-dimensional bodies) is studied adopting a matrix approach, which is particularly useful for numerical applications. The kinematic, static and constitutive equations, once composed, provide an operator equation which has as its unknown the generalized displacement vector. Moreover, constant reference is made to duality, i.e. to the strict correspondence between statics and kinematics that emerges as soon as the corresponding operators are rendered explicit, and it is at once seen how each of these is the adjoint of the other. In this context the finite element method is illustrated as a method of discretization and interpolation for the approximate solution of elastic problems.

The theory of beam systems (statically determinate, statically indeterminate and hypostatic) is then presented, with the solution of numerous examples and the plotting of the corresponding diagrams of axial force, shearing force and bending moment, obtained both analytically and graphically. For the examination of framed structures, approached on the basis of the method of displacements, automatic computation procedures, normally involving the use of computers, are introduced in both the static and the dynamic regime. In addition, the energy aspects and their usefulness in reaching solutions are emphasized.

Finally, the more frequently occurring phenomena of structural failure are studied: instability of elastic equilibrium, plastic collapse and brittle fracture. The unifying aspects, such as those regarding post-critical states and the discontinuous phenomena of snap-back and snap-through, are underlined. Numerous examples regarding frames previously examined in the elastic regime are once more taken up and analyzed incrementally in the plastic regime. Furthermore, comparison of the results based on the theorems of plastic limit analysis (the static and kinematic theorems) is made. As regards fracture mechanics, the conceptual distinction between ‘concentration’ and ‘intensification’ of stresses is highlighted, and the stress treatment and energy treatment are set in direct correlation.

The book has been written to be used as a text for graduate or undergraduate students of either architecture or engineering, as well as to serve as a useful reference for research workers and practising engineers. A suitable selection of various chapters may constitute a convenient support for different types of courses, from the more elementary to the more advanced, and from short monographic seminars to courses covering an academic year.

The mechanics of linear elastic solids (beams, plates, shells, three-dimensional bodies) is studied adopting a matrix approach, which is particularly useful for numerical applications. The kinematic, static and constitutive equations, once composed, provide an operator equation which has as its unknown the generalized displacement vector. Moreover, constant reference is made to duality, i.e. to the strict correspondence between statics and kinematics that emerges as soon as the corresponding operators are rendered explicit, and it is at once seen how each of these is the adjoint of the other. In this context the finite element method is illustrated as a method of discretization and interpolation for the approximate solution of elastic problems.

The theory of beam systems (statically determinate, statically indeterminate and hypostatic) is then presented, with the solution of numerous examples and the plotting of the corresponding diagrams of axial force, shearing force and bending moment, obtained both analytically and graphically. For the examination of framed structures, approached on the basis of the method of displacements, automatic computation procedures, normally involving the use of computers, are introduced in both the static and the dynamic regime. In addition, the energy aspects and their usefulness in reaching solutions are emphasized.

Finally, the more frequently occurring phenomena of structural failure are studied: instability of elastic equilibrium, plastic collapse and brittle fracture. The unifying aspects, such as those regarding post-critical states and the discontinuous phenomena of snap-back and snap-through, are underlined. Numerous examples regarding frames previously examined in the elastic regime are once more taken up and analyzed incrementally in the plastic regime. Furthermore, comparison of the results based on the theorems of plastic limit analysis (the static and kinematic theorems) is made. As regards fracture mechanics, the conceptual distinction between ‘concentration’ and ‘intensification’ of stresses is highlighted, and the stress treatment and energy treatment are set in direct correlation.

The book has been written to be used as a text for graduate or undergraduate students of either architecture or engineering, as well as to serve as a useful reference for research workers and practising engineers. A suitable selection of various chapters may constitute a convenient support for different types of courses, from the more elementary to the more advanced, and from short monographic seminars to courses covering an academic year.

### MSC:

74-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids |

74Kxx | Thin bodies, structures |

74S05 | Finite element methods applied to problems in solid mechanics |