...P. A. Gradin; P. Isaksson; M. Gulliksson The conditions under which force vectors and corresponding displacement vectors become co-linear are investigated under the assumption of a linear elastic structure and for an arbitrary number of loading points. It is shown that there exist an infinite...

...Kees Wapenaar; Jacob Fokkema We thank Stefan Stijlen for bringing the singularity of matrix C to our attention. 07 07 2010 17 08 2010 differential equations diffusion flow matrix algebra vectors waves Matrix C defined in Appendices C and D is singular...

... the crack potential energy release rate and the well-known vector conservative integral J i ( i = 1 , 2 ) is derived. It is demonstrated that J 1 and J 2 integrals are equally important in solving crack problems. This allows a more rational criterion to be proposed, based on the criterion of maximum energy...

... (the fiber direction) we observe the unit circle c in Fig. 10c . Its defining unit vector n ¯ is 21 n ¯ ( θ ) = ( 0 , cos θ , sin θ ) in ( 1 ′ , 2 ′ , 3 ′ ) components. The tube is loaded by an axial force F and a torque T...

...Kees Wapenaar and; Jacob Fokkema Diffusion, flow, and wave phenomena can each be captured by a unified differential equation in matrix-vector form. This equation forms the basis for the derivation of unified reciprocity theorems for diffusion, flow and wave phenomena. Contributed...

... element analysis integration Newton-Raphson method laminates vectors thermoelasticity thermal stresses elastic deformation The sudden application of a heat flux to a structure modeled as a beam, plate, or shell has the tendency to cause the structure to vibrate. This phenomenon is called...

... for the wavelet-based representation which involve linear system theory, spectral representation of the excitation and of the response vectors, and the wavelet transfer tensor of the system. Numerical results demonstrate the usefulness of the developed analytical procedure. Two kinds of discrete harmonic...

... = f k q 1 , … , q n ¯ , t k = p + 1 , … , n where a ^ k k = p + 1 , … , n are unit vectors, f k q 1 , … , q n ¯ , t k = p + 1 , … , n are known functions of q...

... a change of parameters are obtained. It is shown that the bifurcation (splitting) of double eigenvalues is closely related to the stability, flutter, and divergence boundaries in the parameter space. Normal vectors to these boundaries are derived using only information at a boundary point: eigenvalues...

...M. Zingales, Research Assistant; I. Elishakoff, Professor In this study probabilistic and nonprobabilistic anti-optimization approaches are contrasted to evaluate their relative advantages and disadvantages while solving a mechanical problem in presence of vector uncertainty. The different cases...