Nonlinear Dynamics of Elastic Bodies by Z. Wesolowski PDF

By Z. Wesolowski

ISBN-10: 3211815120

ISBN-13: 9783211815120

ISBN-10: 3709127467

ISBN-13: 9783709127469

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In the special case these operators can reduce to the known function of the material coordinates X" only ; the external loads are then called the "dead" loads. Mind that, while Eqs. 3) has to be specified for any problem under consideration because the external loads in different problems can be different. 2. Elastic Particles. Free and Constrained Elastic Continua. In our presentation we shall interpret the deformation function z (X,·) , restric- C. Wozniak 58 ted to an arbitrary but fixed point X , as the function describing the motion of a sufficiently small piece of the matter, X being the position vector of the mass center of this piece in the reference configuration.

1) for aa I aFk = 0 C< T ~'" reduce to • subscripts k • a being fixed, and the latter equation can be treated as an equation for F k .. ( *). e. the material continuum which is unable to carry the component TRk,. of the stress tensor. , are independent of all components of F , then d F is an arbitrary function and from ( 3. 3) it follows that we have constructed the material continuum in which there are no stresses : TR = 0 . Eqs. 1) reduce to aa/fJF '=0 and the dynamics of such continuum is independent of the material properties of the particles.

Manacorda REF ERENCES 1. , Sul potenziale termodinamico dei solidi elastici omogenei ed isotropi per trasformazioni finite, At- ti R. Accad. Italia 3 14, 529, 1943. 2. , Trasformazioni termoelastiche finite, Mem. II, Ann. Mat. pura Appl. ~. (4), 30, 1, 1949. , Trasformazioni termoelastiche finite, Mem. III, Solidi incomprimibili, Ann. Uat. pura appl. (4), 39, 147, 1955. , Sul potenziale isotermo nella piu generale elasticita di secondo grado per solidi incomprimibili. Ann. Mat. pura appl. (4), 40, 77, 1956.

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Nonlinear Dynamics of Elastic Bodies by Z. Wesolowski

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