K. J. Bathe. Finite element procedures in engineering analysis. Prentice-Hall, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in the modelling of LPV structures by developing an analytical model for our example system. For these systems obtaining pointwise LTI models is relatively straightforward, and more complicated systems could easily be modelled using various approximate methods (such as the finite element method [6]) to obtain finite dimensional models. For the frozen parameter models it is also relatively straightforward to introduce modal transformations to allow physical damping measurements to be incorporate into the model. We also pointed out that this is not the case when we explicitly account for the ....

....into the behaviour of the system to be fully exploited. In many problems a form of modal truncation is applied implicitly by either replacing the infinite dimensional spatial operators of a continuum system with finite dimensional matrix representations, as is done in the finite element method [6], or by measuring the modal parameters directly using experimental modal analysis techniques [29] This implicit modal truncation and its implications are not primarily what we are interested in here; we assume that the given finite dimensional model is sufficiently accurate and attempt to reduce ....

K.J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, N.J, 1982.

....damping and stiffness matrices of the model, it and u are the accelerations, velocities and displacements, and fit) are the time dependent forces. Depending on the formulation used for C, the responses for that equation can be obtained by means of the solutions of the associated eigenproblem [1,10] (6) where 0: is a free vibration frequency and 4; a mode shape. Furthermore, the frequencies and modes allow good insight into the structural model [1,14,23] The dimensions of M and reach many thousands for current applications (such as engine and automobile finite element discretizations) and ....

....on the formulation used for C, the responses for that equation can be obtained by means of the solutions of the associated eigenproblem [1,10] 6) where 0: is a free vibration frequency and 4; a mode shape. Furthermore, the frequencies and modes allow good insight into the structural model [1,14,23]. The dimensions of M and reach many thousands for current applications (such as engine and automobile finite element discretizations) and dimensions as high as 106 have already been reported. The free vibration problem defined in (6) can be efficiently solved in any interval of interest if a ....

Bathe, K.-J. (1982), "Finite Element Procedures in Engineering Analysis", Prentice Hall, Inc., Englewood Cliffs, USA.

....equal, and greater than zero [15, 33] Therefore, the number of eigenvalues in [ R] is simply given by the difference ndR nd; where ndR and nd are the number of negative 1 x 1 plus 2 x 2 pivots in D [11] for rr = and rr = EL, respectively. Such a test, also referred to as Sturm sequence check [3], allows as well the location in the spectrum of any pair (k, 3.4 Spectrum Slicing and Computational Interval A spectrum sl cing strategy is useful when many eigensolutions are required, the eigenvalue distribution is clustered (such that the converge is slow) or the continuation of a given run ....

K.-J. Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall, Engle- wood Cliffs, USA, 1982.

....technique to model deformable objects is to view material as a continuum. In this case, the constitutive laws yield partial differential equations that describe the static and dynamic behavior of the material. These equations are usually solved numerically using the Finite Element Method (FEM) [1] or finite differences [12] Such simulations are typically done offline that is, computers spend minutes or hours to arrive at a single answer or a simulation of a few seconds. Real time simulation of deformable objects is a younger field. The performance of modern computers and graphics ....

....continuous models yield more accurate results. The deformation of an object in such a model is described by a boundary value partial differential equation. For realistic objects, this equation cannot be solved analytically. A standard technique to solve it numerically is the Finite Element Method [1]. Using FEM, an object is subdivided into elements of finite size typically polyhedra and a continuous deformation field within each element is interpolated from the deformation vectors at the vertices. Once the interpolation functions for all the elements are chosen, the deformation vectors ....

[Article contains additional citation context not shown here]

K. J. Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall, New Jersey, 1982.

....the four shape vectors ff k . 2.5.1 Numerical integration We use a Newtonian dioeerential equation: m i d P i = fl i dP i F i (13) as the equation governing the motion of our linear elastic model. This equation is related to the dioeerential equation found in continuum mechanics [3]: M U C U KU = R: 14) Following nite elements theory, the mass M and damping C matrices are sparse matrices that are related to the stored physical properties of each tetrahedron. In our case, we consider that M and C are diagonal matrices, i.e. that mass and damping eoeects are ....

K.-L. Bathe. Finite Element Procedures in Engineering Analysis, Prentice-Hall, 1982.

....for each tetrahedron, we store the Lam# coeOEcients and , the four shape vectors ff k , and the stioeness data. During the simulation, we compute forces for each vertex, edge, triangle, and tetrahedron, and we update the vertex positions from the dioeerential equations of continuum mechanics [3]: M U C U F(U) R: 10) Following nite element theory, the mass M and damping C matrices are sparse matrices that are related to the stored physical properties of each tetrahedron. In our case, we consider that M and C are diagonal matrices, i.e. that mass and damping eoeects are ....

K.-L. Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall, 1982.

....data. During the simulation, we compute forces for each vertex, edge, triangle, and tetrahedron, and we use a Newtonian dioeerential equation to update the vertex positions: d P i = fl i dP i F i (11) This equation is related to the dioeerential equations of continuum mechanics [2]: M U C U F(U) R: 12) Following nite element theory, the mass M and damping C matrices are sparse matrices which are related to the stored physical properties of each tetrahedron. In our case, we consider that M and C are diagonal matrices, i.e. that mass and damping eoeects are ....

K.-L. Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall, 1982.

....enhances the HUMAN FACTORY system [23] NUMERICAL METHOD FOR COMPUTER ANIMATION This section does not describe the finite element theory in detail, but rather introduces those concepts used for computer animation purposes. A comprehensive study of the finite element theory is given in Bathe [6] and Zienkiewicz [36] A summary of the theory of elasticity can be found in Timoshenko and Goodier [32] o o o o o o o o o o o o o o o o o o o o o o o o a. linear elements with zero order continuity o o o o o o o o o o o o o o o o o o o o o o o o o ....

Bathe KJ. Finite element procedures in engineering analysis. Prentice Hall, 1982

....of constitutive relations, withou any approximation. I. INTRODUCTION The variational principle, or the principle of virtual work, for the analyses of solid mecahnics with large strains involved has been treated extensively by Washizu [1] and by, for example, Hill [21, Eringert [3] Bathe [4], Malvern [5] Oden [6] Hibbitt et al. 7] McMeeking and Rice [8] Scharnhorst and Pian [9] Lubarda and Lee[10] etc. The virtual work equations can be expressed in rate form and in three incremental forms. In Sec. 2, it is shown that, by starting from any one of the three forms of Cauchy s law ....

....coordinate vector in the undeformed state expressed in Lagrangian coordinates, and N, has the same form as N. Also, the displacements and incremental displacements of a generic point within the element can be linked to the counterparts of the nodal points as (42) Through a very standard procedure [4, 24, 25], the displacement and the incremental displacement gradients can be expressed as (u, Au,o)r=Bn(u, Au, r (43) un. Aur)r = Bra(U; AU, r, 44) where B is a (3 3 3N) matrix than can be obtained through the ape functions and the nodal point coordinates. In the Updated Lagrangian approach, ....

K. 3. Bathe, Finite Element Procedures in Engineering Analysis. Prentice-Hall, Englewood Cliffs, N3 (1982).

....Then we elaborate the construction scheme for the hybrid C C continuous volume interpolation functions designed for our framework. A section on matrix formulation give a recipe for the FEM implementation. All mathematical formulations in this section closely follow the notation of [1]. 3.1 Static Elastomechanics The soft tissue model we use for facial surgery simulation requires the following idealizations: Rather than by explicit application of external body ( or surface ( loading forces soft tissue deformations are invoked by so called prescribed skull displacements ....

.... idealizations: Rather than by explicit application of external body ( or surface ( loading forces soft tissue deformations are invoked by so called prescribed skull displacements obtained from the surgical procedure (see figure 5c) Using this approach reduces so called locking effects [1]. We restrict our model to the laws of linear elasticity, since the displacements and deformations in most craniofacial operations are small in an FEM sense. In addition, we assume the elasticity as being constant, i.e. independent of the stress. Tissue parameters like elasticity and ....

[Article contains additional citation context not shown here]

K.-J. Bathe. Finite element procedures in engineering analysis. Prentice Hall, Englewood Cliffs, 1982.

....w, W3n) are such that the eigenvectors are M orthonormal, which means that TK F and TM I. The eigenvector b is the i th shape vector and w is the associated vibration frequency. Finding the eigenmodes of the damping matrix C is possible if it is defined as a Caughey p 1 series [8]: C = MEk=0 ak[M K] k. If p= 2 then C = a0M aK and equa tion 17 simplifies to a C 2, r, where Q = aoI a 2. This 26 equation system is made of 3n independent equations that can be resolved by discretizing the time. Nastar and Ayache [72] use Pentland and Sclaroff s modal analysis ....

K. Bathe. Finite Element Procedures in Engineering Analysis. Prentice Hall,

No context found.

K. J. Bathe. Finite element procedures in engineering analysis. Prentice-Hall, 1982.

No context found.

K. J. Bathe. Finite element procedures in engineering analysis. Prentice-Hall, 1982.

No context found.

Bathe K J. Finite Element Procedures in Engineering Analysis. Prentice-Hall Inc, Englewood Cliffs, New Jersey, USA, 1982.

No context found.

K. Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall, 1982.

No context found.

K. Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall, 1982.

No context found.

Klaus-Jrgen Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall, 1982.

No context found.

K.-L. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cli#s, NJ, 1982.

No context found.

K-L. Bathe. Finite Element Procedures in Engineering Analysis. PrenticeHall, 1982.

No context found.

Bathe, K.-J. Finite Element Procedures in Engineering Analysis. PrenticeHall, Englewood Cliffs, N.J., 1982.

No context found.

Bathe, R.J. (1982) Finite Element Procedures in Engineering Analysis, Prentice-Hall, New Jersey.

No context found.

K.J. Bathe. Finite Element Procedures in Engineering Analysis. PrenticeHall, Englewood Cli#s, N.J, 1982.

No context found.

K. J. Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall, New Jersey, 1982.

No context found.

K. J. Bathe, Finite Element Procedures in Engineering Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1982).

No context found.

K. J. Bathe, Finite Element Procedures in Engi- neering Analysis. Englewood Cliffs, N J: Prentice- Hall, 1982.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC