Read e-book online Computational mechanics in structural engineering : recent PDF

By Franklin Y Cheng; Yuanxian Gu

ISBN-10: 0080430082

ISBN-13: 9780080430089

Show description

Read Online or Download Computational mechanics in structural engineering : recent developments PDF

Similar mechanics books

Download e-book for kindle: Fundamentals of the Theory of Plasticity (Dover Books on by L. M. Kachanov

Meant to be used via complex engineering scholars and training engineers, this quantity specializes in the plastic deformation of metals at common temperatures, as utilized to the energy of machines and constructions. It covers difficulties linked to the distinct nature of plastic country and critical purposes of plasticity idea.

Richard E. Wilde's Statistical Mechanics: Fundamentals and Modern Applications PDF

Statistical Mechanics displays the most recent innovations and advancements in statistical mechanics. masking numerous strategies and subject matters - molecular dynamic equipment, renormalization idea, chaos, polymer chain folding, oscillating chemical reactions, and mobile automata. 15 machine courses written in FORTRAN are supplied to demonstrate the innovations in addition to greater than a hundred chapter-end workouts.

Additional info for Computational mechanics in structural engineering : recent developments

Example text

Through complicated finite element analysis, see [3,9], we can obtain the following results: the ~ _k'~_~'9... ~ I I I I. l~,~%~kNI I IkN~'~ ~ I I I I i I I I i I I tJ I ! ~-N~I~X'-'~ll I I ',,~~k"~ ' ~ ~ k ' ~ III III II! ill l l l l l l l ~ ~ lllllll~l~-~C~ I I I I 1 ~ ] ~ 1 I ! 6697 175017 1143604 0 Fig. ,~,m L2(a) where C and A are constants independent of (26) h, e and ~ , and (28) FE COMPUTATION OF u Mh(x) IrE Computation o f Uho° (X) According to Eqn. 12, the next step of computing u Mh(x) is to solve the homogenized FE vitual work equation ( 19 )to obtain ,0h°(x).

7. ~, in the formulations ( 31 )--( 35 ). 8. Evaluate the approximate displacements M(x) e h~ u Mh(x) in formulation ( 12 ) , the strains in formulation ( 36 ), and the stresses cr~ (x) in formulation ( 37 ). Numerical Results We have coded the computing program of the FE method based on TSA for 2-dimension case, and made some numerical experiments to verify its effectiveness. Here are some numerical results. The structure is a cantilever investigated by us; the macroscopic model is shown in Fig.

The first step is to introduce the Hamiltonian system theory into the fundamental equations, and the longitudinal coordinate x is treated analogous to the time coordinates (Zhong and Yang, 1991); thus (') represents 0( ) / & . X. A. TABLE 1 ANALOG Y RELATIONSHIP BETWEEN PLANE ELASTICITY AND PLATE BENDING Plane elasticity Airy stress function Plate bending Deflection w ( x , y ) tp Displacement vector u,v Strain Bending moment fimction vector qbx,~y Bending moment e x , ~,y ,'~ xy ; Ou Ov Ou Ov My OdOx M x = M y , M x ,2 Mxy ; O' y ,2 M xy = O, x + : Ox' er x 02(1) 02(p 02(p ~y 2 ' er Y O~ 2 ' T"xy ~X~ 02W 02W Ky "-" OY2 ,K x : ~~X, 2 I~2xY -- Stress-strain relation, ex = (erx - Very) / E ,ey = (Cry - Verx) / E Ox O2W OxOy Bending moment-curvature relation M y = O(K:y + VKx), Mx = D ( K x + V K y ) , 2 M xy = 2 ( 1 - v ) DK xy 7xy = Xxy2(1 + v) / E The principle of minimum potential energy Determined displacement boundary s u, u=u-, Oy Deflection-curvature relation Stress function-stress relation The principle of minimum" complementary energy Given force boundary s m , m v=v Cs=¢s, Determined force boundary s~, Given displacement boundary s w, Ky COSO~ -1- l(xy sincz = 0 cr x cosc~ + Xxy sina = 0 K xy cos or + ~:x sin cz = 0 x xy cosa + ~y sin a = 0 Pro-H-R variational principle H-R variational principle Null moment functions H-R variational principle Pro-H-R variational principle Rigid body translation of Eqn.

Download PDF sample

Computational mechanics in structural engineering : recent developments by Franklin Y Cheng; Yuanxian Gu


by Daniel
4.0

Rated 4.05 of 5 – based on 12 votes