By K. K. Choi, Nam-Ho Kim
Structural layout sensitivity research issues the connection among layout variables to be had to the layout engineer and structural responses decided through the legislation of mechanics. The dependence of reaction measures akin to displacement, rigidity, pressure, typical frequency, buckling load, acoustic reaction, frequency reaction, noise-vibration-harshness (NVH), thermo-elastic reaction, and fatigue existence at the fabric estate, sizing, part form, and configuration layout variables is outlined during the governing equations of structural mechanics. during this 2-volume set, first- and moment- order layout sensitivity analyses are provided for static and dynamics responses of either linear and nonlinear elastic structural platforms, together with elasto-plastic and frictional touch problems.
Book 2 covers layout sensitivity research of nonlinear structural platforms utilizing continuum layout sensitivity research equipment. It additionally discusses functional layout instruments and functions; sizing and form layout parameterization, layout pace box computation, numerical implementation of the sensitivity for general-purpose code improvement, and numerous different sensible layout applications.
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Sample text
8 illustrates a general contact condition with a rigid surface in R2. Since the motion of the rigid surface is prescribed throughout the analysis, a natural coordinate[ is used to represent 480 8. Nonlinear Structural Analysis the location on a rigid surface. The coordinates of contact point xc can be represented using a natural coordinate at the contact point [c by xc ([c ). 158) The impenetrability condition can be imposed on the structure by measuring the distance between a part of the structural boundary *c and the rigid surface, as shown in Fig.
140) p where V0 is the initial yield stress of a uniaxial tension test, and Kˆ ,e ( e p ) is the isotropic p hardening law. ep is an effective plastic strain and can be determined using the uniaxial tension test as ³ ep t 2 3 0 e p (W ) dW . 141) The internal variables are reduced to the effective plastic strain and back stress. 144) which is a nonlinear equation with respect to Jˆ . 144) can be solved using a local Newton method to compute Jˆ . 120) guarantees the stability of this return-mapping method, which is a contraction mapping.
Thus, linearization of the tangential slip variational form has to be separated into stick and slip conditions. 189) implicitly depends on displacement through Q, gt, and et. 190) Q etT 'z. 191) en (etT 'z ). 177). 187) leads to the tangential stick bilinear form as bT* ( z; 'z , z ) Zt ³ Q 2 z T et etT 'z d * *c DQ gt z T (en etT et enT )'z d * c Q gt 2 Zt ³ (J t 2DE ) g n E t z T et etT 'z d *. 192) as b* ( z; 'z , z ) bN* ( z; 'z , z ) bT* ( z; 'z , z ). 193) is symmetric with respect to the incremental displacement and variation of displacement.
