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The Finite Element Method: Linear Static and Dynamic Finite by Thomas J. R. Hughes

By Thomas J. R. Hughes

This textual content is aimed toward helping engineering and actual technological know-how scholars in cultivating accomplished abilities in linear static and dynamic finite point method. in line with classes taught at Stanford collage and the California Institute of expertise, it levels from primary ideas to functional computing device implementations. extra sections comment on the frontiers of analysis, making the e-book of strength curiosity to more matured analysts and researchers operating within the finite point field.

In addition to its exam of various typical elements of the finite aspect procedure, the amount comprises many distinct elements, together with a accomplished presentation and research of algorithms of time-dependent phenomena, plus beam, plate, and shell theories derived at once from 3-dimensional elasticity concept. It additionally encompasses a systematic therapy of "weak," or variational, formulations for various sessions of initial/boundary-value problems.

Directed towards scholars with no in-depth mathematical education, the textual content contains introductory fabric at the mathematical concept of finite parts and lots of vital mathematical effects, making it an incredible primer for extra complex works in this subject.

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Extra resources for The Finite Element Method: Linear Static and Dynamic Finite Element Analysis

Sample text

Any point along the normal consolidation line represents the stress state of a normally consolidated (NC) soil. Also, any point along an unloading–reloading line represents an overconsolidated stress state. 86. This point has an overconsolidated stress state since the soil was previously subjected to a preconsolidation pressure of pB = 30 kPa. In fact, the overconsolidation ratio at point C is OCR = pB /pC = 30 kPa/1 kPa = 30, which means that the soil at point C is heavily overconsolidated. 8, known as the critical-state condition.

Dεes = 0). 33) is reduced to dεs = dεs . It is important to note that the following equations are given in incremental forms and thus need to be used in an incremental manner: The load must be applied in small increments and the corresponding strain increments are calculated. The strain increments are accumulated to give us the total strain. 38), we can predict the stress–strain behavior of a normally consolidated (NC) clay. The stress is applied using a given stress path, and the corresponding strains are calculated.

During that time the yield surface grows (strain hardening) until the effective stress path touches the critical-state line at point 5, where failure occurs. 16b. If line 2–5 were not horizontal in the e–p plane, there would be a change in the void ratio, which is not admissible in this undrained condition. 16 describes the stress state at failure. 16b, point 5 has a void ratio ef (on the critical-state line) which is identical to the initial void ratio e0 at point 3. 41) where pf is the mean effective stress at failure.

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