Download A Finite Element Method for Plane Stress Problems with Large by Kirchner E., Reese St., Wriggers P. PDF

By Kirchner E., Reese St., Wriggers P.

A two-dimensional finite point procedure is built for big deformation plasticity. important axes are used for the outline of the fabric behaviour, and using central logarithmic stretches results in precise formulae for finite deformation issues of huge elastic and plastic lines. a good go back mapping set of rules and the corresponding constant tangent are derived and utilized to airplane tension difficulties. examples convey the functionality of the proposed formula.

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Extra info for A Finite Element Method for Plane Stress Problems with Large Elastic and Plastic Deformations

Example text

1:131Þ where I is the 2  2 identity matrix. The acceleration vector of Equation 107 can also be written as ! €rO €r ¼ ½ I Ah u  Š € ÿ h_2 A u h ð1:132Þ Substituting Equations 131 and 132 into Equation 129 and using Equation 113, which is the result of using the center of mass as the reference point, one obtains  dW i ¼ drTO dh à mI 0 0 IO ! €rO h€ ! ð1:133Þ where m is the mass of the rigid body and I O is the mass moment of inertia about the center of mass that was used in Equation 117. The virtual work of all the applied forces and moments acting on the body can be written as  dW e ¼ FT drO þ MO dh ¼ drTO dh à F MO !

Again, Equations 110 and 111 are also applicable to the spatial rigid-body motion. The only difference is in the definition of the transformation matrix and the angular velocity and angular acceleration vectors, which depend on three rotation parameters instead of one as will be discussed in Chapter 7. Application of D’Alembert’s Principle D’Alembert’s principle is the foundation for the skillful development of the principle of virtual work made by Lagrange. D’Alembert’s principle states that the inertia forces can be treated as the applied external forces.

Therefore, these coordinates depend on time. If these coordinates are determined, the global position of any point on the body, or equivalently the body configuration, can be determined using the preceding equation. An equation in the same form as Equation 100 can be obtained in the case of spatial motion of rigid bodies, as will be demonstrated in Chapter 7. In the case of spatial motion, three-dimensional vectors instead of two-dimensional vectors are used, and the transformation matrix A is expressed in terms of three independent rotation parameters instead of one parameter.

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