Variational formulation of linear problems with nonhomogeneous boundary conditions and internal discontinuities
A variational formulation applicable to linear operators with nonhomogeneous boundary conditions and jump discontinuities is presented. For the formulation to be applicable, the boundary condition and discontinuities have to be consistent with the operator governing the field problem. The problem is...
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Published in | Computer methods in applied mechanics and engineering Vol. 7; no. 1; pp. 75 - 91 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
1976
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Abstract | A variational formulation applicable to linear operators with nonhomogeneous boundary conditions and jump discontinuities is presented. For the formulation to be applicable, the boundary condition and discontinuities have to be consistent with the operator governing the field problem. The problem is set up in a space of suitable continuous bilinear mapping. Thus, operators on inner product spaces, convolution spaces and energy spaces are included as specializations. The basic construction can be used to generate dual-complementary variational principles. Implementation is illustrated by examples. The role of boundary terms in finite element discretizations based on interpolants of limited smoothness is discussed. |
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AbstractList | A variational formulation applicable to linear operators with nonhomogeneous boundary conditions and jump discontinuities is presented. For the formulation to be applicable, the boundary condition and discontinuities have to be consistent with the operator governing the field problem. The problem is set up in a space of suitable continuous bilinear mapping. Thus, operators on inner product spaces, convolution spaces and energy spaces are included as specializations. The basic construction can be used to generate dual-complementary variational principles. Implementation is illustrated by examples. The role of boundary terms in finite element discretizations based on interpolants of limited smoothness is discussed. A variational formulation applicable to linear operators with nonhomogeneous boundary conditions and jump discontinuities is presented. For the formulation to be applicable, the boundary condition and discontinuities have to be consistent with the operator governing the field problem. The problem is set up in a space of suitable continuous bilinear mapping. Thus, operators on inner product spaces, convolution spaces and energy spaces are included as specializations. The basic construction can be used to generate dual-complementary variational principles. Implementation is illustrated by examples. The role of boundary terms in finite element discretization based on interpolants of limited smoothness is discussed. |
Author | Sandhu, Ranbir S. Salaam, U. |
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Cites_doi | 10.1016/0020-7225(74)90073-1 10.1007/BF01262691 10.1090/qam/99951 10.1007/BF00248489 10.1007/BF02153074 10.1016/0020-7225(70)90081-9 10.1002/nme.1620010103 10.1016/0020-7683(68)90081-4 10.1016/0020-7683(71)90085-0 |
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References | Magri (BIB20) 1972 Oden (BIB7) 1972 Mikhlin (BIB4) 1970 Pian (BIB11) 1972 Tonti (BIB10) 1967; 2 Gurtin (BIB14) 1964; 16 Gurtin (BIB13) 1963; 13 Oden (BIB18) 1971 Arthurs (BIB9) 1970 Tikhonov, Samarskii (BIB27) 1963 Prager (BIB24) 1967 Oden, Reddy (BIB12) 1974; 12 Tonti (BIB8) 1972 Salaam (BIB28) 1974 Pian, Tong (BIB29) 1969; 1 Tonti (BIB19) 1972 Washizu (BIB22) 1968 Gurtin (BIB15) 1964; 12 Sandhu, Pister (BIB17) 1971; 7 Vainberg (BIB5) 1964 Finlayson (BIB6) 1972 Nemat-Nasser (BIB26) 1974 Mikhlin (BIB1) 1965 Reissner (BIB21) 1958; 8 Sandhu, Pister (BIB16) 1970; 8 Mikhlin (BIB2) 1964 Prager (BIB25) 1968; 4 Nickelland, Sackman (BIB23) 1968; 26 Mikhlin (BIB3) 1971 Gurtin (10.1016/0045-7825(76)90006-2_BIB15) 1964; 12 Salaam (10.1016/0045-7825(76)90006-2_BIB28) 1974 Mikhlin (10.1016/0045-7825(76)90006-2_BIB2) 1964 Mikhlin (10.1016/0045-7825(76)90006-2_BIB3) 1971 Nickelland (10.1016/0045-7825(76)90006-2_BIB23) 1968; 26 Prager (10.1016/0045-7825(76)90006-2_BIB25) 1968; 4 Tonti (10.1016/0045-7825(76)90006-2_BIB19) 1972 Washizu (10.1016/0045-7825(76)90006-2_BIB22) 1968 Vainberg (10.1016/0045-7825(76)90006-2_BIB5) 1964 Tonti (10.1016/0045-7825(76)90006-2_BIB10) 1967; 2 Tikhonov (10.1016/0045-7825(76)90006-2_BIB27) 1963 Mikhlin (10.1016/0045-7825(76)90006-2_BIB1) 1965 Pian (10.1016/0045-7825(76)90006-2_BIB11) 1972 Oden (10.1016/0045-7825(76)90006-2_BIB18) 1971 Oden (10.1016/0045-7825(76)90006-2_BIB12) 1974; 12 Nemat-Nasser (10.1016/0045-7825(76)90006-2_BIB26) 1974 Sandhu (10.1016/0045-7825(76)90006-2_BIB17) 1971; 7 Tonti (10.1016/0045-7825(76)90006-2_BIB8) 1972 Reissner (10.1016/0045-7825(76)90006-2_BIB21) 1958; 8 Arthurs (10.1016/0045-7825(76)90006-2_BIB9) 1970 Mikhlin (10.1016/0045-7825(76)90006-2_BIB4) 1970 Pian (10.1016/0045-7825(76)90006-2_BIB29) 1969; 1 Magri (10.1016/0045-7825(76)90006-2_BIB20) 1972 Prager (10.1016/0045-7825(76)90006-2_BIB24) 1967 Gurtin (10.1016/0045-7825(76)90006-2_BIB14) 1964; 16 Sandhu (10.1016/0045-7825(76)90006-2_BIB16) 1970; 8 Gurtin (10.1016/0045-7825(76)90006-2_BIB13) 1963; 13 Finlayson (10.1016/0045-7825(76)90006-2_BIB6) 1972 Oden (10.1016/0045-7825(76)90006-2_BIB7) 1972 |
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Eng. contributor: fullname: Tong – year: 1968 ident: BIB22 article-title: Variational methods in elasticity and plasticity contributor: fullname: Washizu – volume: 2 start-page: 201 year: 1967 end-page: 209 ident: BIB10 article-title: Variational principles in elastostatics publication-title: Meccanica contributor: fullname: Tonti – year: 1972 ident: BIB19 article-title: On the variational formulation for linear initial value problems publication-title: Report Instituto di Matematica del Politechnico di Milano 32-20133 contributor: fullname: Tonti – year: 1972 ident: BIB20 article-title: Variational formulation for any linear eqiation publication-title: Variational methods in engineering contributor: fullname: Magri – year: 1970 ident: BIB4 article-title: An advanced course in mathematical physics contributor: fullname: Mikhlin – volume: 8 start-page: 989 year: 1970 end-page: 999 ident: BIB16 article-title: A variational principle for linear coupled field problems publication-title: Int. 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Rat. Mech. Anal. doi: 10.1007/BF01262691 contributor: fullname: Gurtin – year: 1971 ident: 10.1016/0045-7825(76)90006-2_BIB3 contributor: fullname: Mikhlin – volume: 12 start-page: 252 year: 1964 ident: 10.1016/0045-7825(76)90006-2_BIB15 article-title: Variational principles for linear initial value problems publication-title: Quar. App. Math. doi: 10.1090/qam/99951 contributor: fullname: Gurtin – year: 1964 ident: 10.1016/0045-7825(76)90006-2_BIB5 contributor: fullname: Vainberg – volume: 26 start-page: 11 year: 1968 ident: 10.1016/0045-7825(76)90006-2_BIB23 article-title: Variational principles for linear coupled thermoelasticity publication-title: App. Math. contributor: fullname: Nickelland – year: 1963 ident: 10.1016/0045-7825(76)90006-2_BIB27 contributor: fullname: Tikhonov – year: 1970 ident: 10.1016/0045-7825(76)90006-2_BIB4 contributor: fullname: Mikhlin – year: 1972 ident: 10.1016/0045-7825(76)90006-2_BIB19 article-title: On the variational formulation for linear initial value problems publication-title: Report Instituto di Matematica del Politechnico di Milano 32-20133 contributor: fullname: Tonti – year: 1972 ident: 10.1016/0045-7825(76)90006-2_BIB8 article-title: A systematic approach to the search for variational principles contributor: fullname: Tonti – year: 1970 ident: 10.1016/0045-7825(76)90006-2_BIB9 contributor: fullname: Arthurs – volume: 16 start-page: 234 year: 1964 ident: 10.1016/0045-7825(76)90006-2_BIB14 article-title: Variational principles in linear elastodynamics publication-title: Arch. Rat. Mech. Anal. doi: 10.1007/BF00248489 contributor: fullname: Gurtin – year: 1965 ident: 10.1016/0045-7825(76)90006-2_BIB1 contributor: fullname: Mikhlin – year: 1972 ident: 10.1016/0045-7825(76)90006-2_BIB7 article-title: Variational principles in nonlinear continuum mechanics contributor: fullname: Oden – volume: 2 start-page: 201 year: 1967 ident: 10.1016/0045-7825(76)90006-2_BIB10 article-title: Variational principles in elastostatics publication-title: Meccanica doi: 10.1007/BF02153074 contributor: fullname: Tonti – volume: 8 start-page: 989 year: 1970 ident: 10.1016/0045-7825(76)90006-2_BIB16 article-title: A variational principle for linear coupled field problems publication-title: Int. J. Eng. 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