By John T. Katsikadelis
Boundary aspect process for Plate Analysis bargains one of many first systematic and targeted remedies of the applying of BEM to plate research and layout.
Aiming to fill within the wisdom gaps left via contributed volumes at the subject and bring up the accessibility of the huge magazine literature overlaying BEM utilized to plates, writer John T. Katsikadelis attracts seriously on his pioneering paintings within the box to supply a whole advent to concept and application.
Beginning with a bankruptcy of initial mathematical historical past to make the ebook a self-contained source, Katsikadelis strikes directly to disguise the applying of BEM to easy skinny plate difficulties and extra complex difficulties. each one bankruptcy comprises numerous examples defined intimately and closes with difficulties to resolve. proposing the BEM as an effective computational strategy for useful plate research and layout, Boundary point approach for Plate Analysis is a priceless reference for researchers, scholars and engineers operating with BEM and plate demanding situations inside of mechanical, civil, aerospace and marine engineering.
- One of the 1st assets devoted to boundary aspect research of plates, delivering a scientific and available introductory to conception and application
- Authored via a number one determine within the box whose pioneering paintings has ended in the improvement of BEM as an effective computational process for sensible plate research and design
- Includes mathematical historical past, examples and difficulties in a single self-contained resource
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Boundary point process for Plate research bargains one of many first systematic and exact remedies of the applying of BEM to plate research and layout. Aiming to fill within the wisdom gaps left through contributed volumes at the subject and bring up the accessibility of the wide magazine literature overlaying BEM utilized to plates, writer John T.
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Extra info for The boundary element method for plate analysis
1 2 r ln rrdq ¼ 0 8pD ! 0 Gr @n 2p Z 0 2p ! 81c) Z 2p ! 81d) Substituting the above limits into Eq. 82) and in the limit Eq. 78) gives the integral representation of the solution in W in the form Z w ðP Þ ¼ W v ðP, QÞf ðQ ÞdWQ ! 83) 50 BEM for Plate Bending Analysis where P, Q 2 W, q 2 G. The subscript in the differentials dW, ds and in the @ , M , V , T indicates the point with respect to which integration operators @n or differentiation is performed. Except where it is required for clarification, the arguments of the functions and subscripts in Eq.
A plate with a boundary of arbitrary shape and having corners will be considered (Fig. 1). The plate is subjected to transverse load density f ðx, yÞ and edge load densities M Ãn ,V Ãn . Moreover, a concentrated transverse load RÃk ðk ¼ 1,2, ... ,K Þ may be applied at a corner k (Fig. 2). The boundary of the plate may be elastically supported in the transverse direction on springs with translational stiffness k T ðs Þ as well as elastically restrained by springs having rotational stiffness k R ðs Þ.
35b) Eq. 36) i Xh Á k cðk Þ w k À Rk∗ dw k ¼ 0 Q n + k G w À V n∗ dwds + k Moreover, noting that w ,t ¼ w ,s and M nt is discontinuous at the corner points, the integration by parts of the last term in the first line integral of Eq. 37) G G k ð+Þ ð ÀÞ where ½½M nt k ¼ M nt À M nt designates the jump of discontinuity of the twisting moment at the corner point k. Thus, Eq. 38) i Xh k ðck Þ w k À ½½M nt k À RÃk dw k ¼ 0 k Inasmuch as the quantities dw, dw ,n and dw k are arbitrary, Eq. 40c) It should be noted that the star superscript denotes a prescribed quantity.