By K. K. Choi, Nam-Ho Kim
ISBN-10: 0387233369
ISBN-13: 9780387233369
Wide numerical tools for computing layout sensitivity are incorporated within the textual content for useful program and software program improvement. The numerical technique permits integration of CAD-FEA-DSA software program instruments, in order that layout optimization will be conducted utilizing CAD geometric versions rather than FEA versions. This strength permits integration of CAD-CAE-CAM in order that optimized designs should be synthetic successfully.
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Extra resources for Structural Sensitivity Analysis and Optimization 2, Nonlinear Systems and Applications
Sample text
104) where Wi,j = ('zi,j 'zj,i)/2 is a component of the spin tensor that represents a rigid body rotational motion. 104), where Ej is a material unit vector. 105) where ei is a unit vector in the ith direction of Cartesian coordinates. 106) J ij ( 'V V kjWik V ikWkj ) ei e j , where 'V ijJ is the Jaumann or co-rotational Cauchy stress increment, which is the objective rate because it takes an increment of the tensor with respect to the principal axis 470 8. Nonlinear Structural Analysis of the deformation rate tensor.
The near-incompressibility of hyperelastic material can be imposed by using the bulk modulus of a large magnitude, which relates the volumetric stress to the strain. Although a very simple material model is discussed here, the method can be extended to general hyperelastic material models. 60) where C10, C01 are the material constants, and K is the bulk modulus. For a small strain, 2(C10 + C01) represents the shear modulus, and 6(C10 + C01) represents the equivalent Young’s modulus for a three-dimensional solid structure, and 8(C10 + C01) represents Young’s modulus for a two-dimensional solid structure.
But in the case of a small slip (microdisplacement), traction force is proportional to the tangential slip. The penalty parameter Zt is a constant for this case. An exact stick condition represented by a step function in the classical Coulomb friction law is now regularized by a piecewise linear function, with the penalty parameter Zt serving as a regularization parameter. As shown in Fig. 9, this regularized friction law is reduced to the classical law as Zt ĺ f. A regularized stick condition occurs when Zt gt d PZn g n .
Structural Sensitivity Analysis and Optimization 2, Nonlinear Systems and Applications by K. K. Choi, Nam-Ho Kim
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