Elastic Structural Deformation Decomposition And Basic Application

The deformation information is the important basis of engineering structure analysis,design,maintenance and reinforcement.In terms of space scale,the deformation includes many microcosmic basic deformation forms based on the elastic theory,such as normal strain and shear strain.Besides,the deformation includes many macroscopic basic deformation forms based on the material mechanics,such as bending and torsion.With the aid of commercial finite element software,laboratory test and field test,the microcosmic basic deformation forms under the effect of various environments can be obtained conveniently,such as normal strain and shear strain.At the same time,comprehensive macroscopic deformations can be also obtained,such as lateral deformation,deflection and deformation between the layers.But a convenient deformation conversion method is lacked between microcosmic deformations and macroscopic deformations.The convenient deformation conversion method is also lacked between comprehensive deformations and basic deformations.Supported by the National Natural Science Founding of China(50978232),elastic structure deformation decomposition method based on theory of orthogonal decomposition is put forward.The comprehensive deformations can be decomposed into the basic deformations by the method.The macroscopic deformations can be also decomposed into the microcosmic deformations by the method.In the plane problems,the basic deformation characteristics of three nodes equilateral triangle unit are analyzed.The corresponding complete orthogonal mechanical deformation bases can be obtained.Taking an example of skew girder,the macroscopic bending deformation can be decomposed into microscopic tension deformation and microscopic compression deformation.Secondly,the macroscopic basic deformation characteristics of four nodes square unit are analyzed.The corresponding complete orthogonal mechanical deformation bases can be obtained.Taking an example of simply supported beam,the comprehensive deformation of beam can be decomposed into rigid body displacement and the basic deformations,such as tension and compression,bending and shear.Then,based on complete orthogonal mechanical deformation bases of four point square element and considering effect of poisson's ratio,the corresponding complete physical deformation bases can be obtained.Taking an example of both ends hinged beam,accurate analysis of plane structure deformation decomposition is realized.At the same time,the engineering accuracy of the deformation decomposition by complete orthogonal mechanical deformation bases is verified.In the space problems,the basic deformation characteristics of six nodes equilateral three prism unit are analyzed.The corresponding complete orthogonal mechanical deformation bases can be obtained.Taking an example of skew slab bridge,the mutual conversion between the macroscopic space deformation and the microscopic space deformation can be realized.Furthermore,the basic deformation characteristics of eight nodes equilateral cube unit are analyzed.The corresponding complete orthogonal mechanical deformation bases can be obtained.Taking an example of thin plate,it is proved that torsion-reverse shear coupling deformation is the macroscopic deformation form which is orthogonal with other deformation forms,such as tension and compression,bending and shear.To further verify the validity of the deformation decomposition,the following basic applied problems are studied.Firstly,the deformation decomposition of torsion component is analyzed.The pure torsion deformation of torsion cylinder can be identified.This suggests that the pure torsion deformation is a deformation form that occurs in particular situation.The warpage deformation of free torsion cube is made up of the 50%torsion deformation and the 50%reverse shear deformation.Secondly,degradation problems of basic deformation can be studied.With the refining of unit division,macroscopic basic deformation forms will gradually be degenerated into microscopic basic deformation forms.For example,the reverse bending deformation will be gradually degenerated into tension deformation,compression deformation and shear deformation.Torsion shear deformation will be gradually degenerated into shear deformation.Thirdly,the deformation decomposition theory can be applied to the decomposition of the modal relative deformation.The structure modal quantitative analysis can be realized.Especially,the shear mode and the coupling model can be identified quantitatively.