In engeneering practice,shell and board on the elastic foundation usually are simplified as beam on elastic foundation.In fact,the stress anasysis of beam on elastic foundation is the anasysis of soil and structure interaction.So it is necessary to study the stress of the beam on elastic foundation under the outer stress. Using the model of the foundation beams with variable sections on bi-parameter elastic foundation,improves the shortages of the Winkler elastic foundation model,and the equivalent sections model.Random beam with variable sections can be discrete into beam with step under the parabolic load ,the model uses transmission matrix.Comparing the stresses and deflections of beam with variable sections on bi-parameter foundation with different G,the solution can accord with the load of foundation and deformation's character.
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