| ^^__text__TEXTgpaS__data__DATA0Rd\__cstring__TEXTVXY__picsymbolstub2__TEXT]7`n<__la_sym_ptr2__DATA^(1ap  __nl_symbol_ptr__DATA^ \a__textcoal_nt__TEXT^ha @tqy PYY\SqUSDEEEE\$J^E}u ]E]D$E$ ^E܃}u^@XE܍]D$E܉$]E}av TNU;EtTNUE䍋RUDE荋RUDE썋RUD$@]D$E܉$!]EEEEԉЋMԙ9EuG]D$E܉$\TNUDD$ ED$I]D$E܉$\EG]D$E܉$\G]D$E܉$}\^@X9Et E܉$I\D[]ÐUST\EEPEUEEEED$Ef8u E@EEEЋEЉ$[EEẼ}}ẼrEf8u@QEPE E@EY[D$E$2[u$\@XD$T$ZUD$E$Ztc[D$E$Zu EE}avb`LUԉDD$E$Zu1`LUԉDD$d[$5ZEEԃ떃}uED$[$ ZEfE@E@M썓\EAE}u-D$D$ D$ED$U$YE$]YE}t}uEEȃT[]assemble ( ) assemble (M, C) Computes and returns the global stiffness matrix by computing the local stiffness matrices and assembling them into the global matrix. For transient problems, if M is specified then it will contain the global mass matrix on return. Similarly, C will contain the global damping matrix. All matrices are compact. clear_nodes ( ) Clears the displacements and equivalent nodal force vectors for all nodes in the current problem. compute_modes (K, M) compute_modes (K, M, X) Compute the modes for the given stiffness matrix, K, and mass matrix, M. The result is the vector of eigenvalues. If X is specified then it will contain the matrix of eigenvectors upon return. compute_stresses (e) Not available yet. construct_forces ( ) construct_forces (t) Constructs and returns the global nodal force vector based on all nodal forces and the global DOFs active at those nodes. For transient problems, t may be a scalar expression used to specify the current time. If t is missing then it is assumed to be zero. find_dofs ( ) Computes the set of active DOFs for the current problem. As a result, the DOF-related fields of the problem structure are initialized. The number of active DOFs is returned. global_dof (n, d) Returns the global DOF corresponding to a local DOF. The local DOF is specified by its node, n, and the DOF, d. The node may be specified as either a node object or a node number. integrate_hyperbolic (K, M, C) Solves the discrete equation of motion, Ma + Cv + Kd = F, using Newmark's method with the Hilbert-Hughes-Taylor alpha correction for improved accuracy with numerical damping. The result is a matrix of nodal displacements, with each column corresponding to a single time step. The sizes of the matrices must be consistent with the definition of the problem. Compact matrices are expected. integrate_parabolic (K, M) Solves the discrete parabolic differential equation Mv + Kd = F using a generalized trapezoidal method. The sizes of the matrices must be consistent with the definition of the problem. Compact matrices are expected. local_dof (g) local_dof (g, l) Returns the number of the node corresponding to the global DOF, g. If l is specified the it will contain the local DOF on return. (The number of the node is returned rather than the node object itself since the nodes may have been renumbered.) remove_constrained (K) Removes the rows and columns of K at all DOFs with a fixed boundary condition and returns the new matrix. K is not modified. K should with be either a symmetric matrix or a column vector. The size of K must be consistent with the definition of the problem. renumber_nodes ( ) Renumbers the nodes of the current problem using the Gibbs-Poole-Stockmeyer and Gibbs-King node renumbering algorithms for bandwidth and profile reduction. The result is a permutation vector of the node numbers. restore_numbers (p) Restores the original node numbering of the current problem. The permutation vector is specified by p. The return value is always null. set_up (e) set_up (e, s) Not available yet. solve_displacements (K, f) Solves the linear system Kd = f for the vector of global nodal displacements. The sizes of the inputs must be consistent with the definition of the problem. Additionally, K and f should both be condensed. K is expected to be compact. zero_constrained (K) Zeroes the rows and columns of K at all DOFs with a fixed boundary condition and returns the new matrix. K is not modified. K should with be either a symmetric matrix or a column vector. If K is a matrix then a one is placed on the corresponding diagonal. The size of K must be consistent with the definition of the problem. abs (X) fabs (X) Computes the absolute value of each element of X. If X is a scalar then the result is a scalar. If X is a matrix then the result is a matrix. ceil (X) Computes the ceiling of each element of X. If X is a scalar then the result is a scalar. If X is a matrix then the result is a matrix. cos (X) Computes the cosine of each element of X. If X is a scalar then the result is a scalar. If X is a matrix then the result is a matrix. exp (X) Computes the exponential of each element of X (e raised to the power X). If X is a scalar then the result is a scalar. If X is a matrix then the result is a matrix. floor (X) Computes the floor of each element of X. If X is a scalar then the result is a scalar. If X is a matrix then the result is a matrix. hypot (X, Y) Computes the square root of X*X+Y*Y. If X and Y represent the lengths of the sides of a right triangle, then the result is the length of the hypotenuse. If X and Y are both scalars then the result is a scalar. If X and Y are both matrices of the same size then the result is a matrix. log (X) Computes the natural logarithm of each element of X. If X is a scalar then the result is a scalar. If X is a matrix then the result is a matrix. log10 (X) Computes the base-10 logarithm of each element of X. If X is a scalar then the result is a scalar. If X is a matrix then the result is a matrix. sin (X) Computes the sine of each element of X. If X is a scalar then the result is a scalar. If X is a matrix then the result is a matrix. sqrt (X) Computes the square root of each element of X. If X is a scalar then the result is a scalar. If X is a matrix then the result is a matrix. tan (X) Computes the tangent of each element of X. If X is a scalar then the result is a scalar. If X is a matrix then the result is a matrix. concat (s, t) Returns the concatenation of s and t, both of which must be strings. eval (s) Not yet implemented. exit ( ) exit (n) Exits the interpreter with exit code n. If n is omitted then zero is used. help ( ) help (s) Requests help on an operation, function, or other topic. If s is omitted then a listing of valid topics is printed. The argument s should be either a string or a function name. history ( ) history (n) Prints the command history list. If n is given then only the last n commands are printed. include (s) Includes the file named by s. The file is included in the global scope. The environment variable BURLAP_PATH is used to search for the file named by s. load (s) Not yet implemented. read ( ) Reads a line from standard input and returns it as a string. A null value is returned upon end of file. reads ( ) Reads a string from standard input and returns it. A null value is returned upon end of file. save (s) Not yet implemented. system (s) Executes the UNIX command named by s. The command is executed in its own subshell. The return status of the command is returned. type (A) Returns a string describing the type of A, which may be of any type. write (...) Writes its arguments followed by a newline to standard output. No spaces are automatically written between the arguments, although each matrix is written on its own line. writes (...) Writes its arguments to standard output. No spaces are automatically written between the arguments, although each matrix is written on its own line. chol (X) Returns the cholesky decomposition, B, of X, such that B*B' = X. B will be lower triangular. X must be symmetric and positive definite. cols (X) Returns the number of columns of X. A scalar is defined to have a single column. compact (X) Returns a compact-storage matrix whose elements are identical to X, which must be a symmetric matrix. The space required by a compact matrix is approximately equal to the number of non-zero entries. The compact representation of a scalar is itself. det (X) Returns the determinant of X, which must be nonsingular. The determinant of a scalar is itself. eig (X) eig (X, V) Return a column vector containing the eigenvalues of X, which must be square. If X is a scalar then X is returned. If a variable V is specified and X is symmetric then V will contain the matrix of eigenvectors on output. Otherwise, V is ignored. eye (m) eye (m, n) Returns an identity matrix of size (m x n). If n is omitted then an (m x m) matrix is returned. Both m and n must be scalars. inv (X) Returns the inverse of X, or (1/X). X must be a either a nonsingular matrix or a non-zero scalar. lu (X) lu (X, L) lu (X, L, U) lu (X, L, U, P) Computes the LU decomposition of X, which must be nonsingular. The return value is row permuted combination of L and U, with the diagonal of L not being stored since L is unit lower triangular. If the remaining parameters are variables then they will contain L, U, and/or P (the permutation matrix) on output, such that P*L*U=X. norm (X) norm (X, s) Returns the norm of X. If X is a scalar then s is ignored and the absolute value of X is returned. If X is a vector then s may be one of "1", "2", or "fro" indicating that the 1-norm, 2-norm, or frobenius-norm (identical to the 2-norm) is to be computed. The default is to compute the 2-norm. If X is a matrix then s may be either "1" or "fro" indicating that the 1-norm or frobenius-norm is to be computed. The default is to compute the frobenius-norm. ones (m) ones (m, n) Returns a matrix of size (m x n) whose elements are all one. If n is not specified then an (m x m) matrix is returned. Both m and n must be scalars. qr (X) qr (X, Q) qr (X, Q, R) Computes the QR decomposition of X, which must be overdetermined (tall and thin). The return value is R, which is right triangular, such that Q'*X=R. If a variable Q is specified then it will contain the orthogonal matrix of the decomposition on output. rand ( ) rand (m) rand (m, n) rand (m, n, s) Returns a matrix of size (m x n) with randomly generated elements between zero and one. If n is omitted then an (m x m) matrix is returned. If both m and n are absent then a random scalar is returned. If s is specified and is non-zero then it used to seed then random number generator. Both m and n must be scalars. rows (X) Returns the number of rows of X. A scalar is defined to have a single row. zeros (m) zeros (m, n) Returns a matrix of size (m x n) whose elements are all zero. If n is not specified then an (m x m) matrix is returned. Both m and n must be scalars. X = Y X := Y Assigns Y to X and returns X. X must be a variable name, a subsection of a matrix (submatrix), or the result of a function call returning a global variable. If X is a submatrix then the dimensions of Y must match the dimensions of X. m || n m or n If m evaluates to true (non-zero) then one is returned. Otherwise, n is evaluated and if n is false then zero is returned. If n is true (non-zero) then one is returned. Both m and n must be scalars. m && n m and n If m evaluates to false (zero) then zero is returned. Otherwise, n is evaluated and if n is false then zero is returned. If n is true (non-zero) then one is returned. Both m and n must be scalars. X == Y Compares each element of X against each element of Y and sets the corresponding element of the result to one if X is equal to Y, and zero otherwise. If both X and Y are matrices then their dimensions must match. X != Y X <> Y Compares each element of X against each element of Y and sets the corresponding element of the result to one if X is not equal to Y, and zero otherwise. If both X and Y are matrices then their dimensions must match. X < Y Compares each element of X against each element of Y and sets the corresponding element of the result to one if X is less than to Y, and zero otherwise. If both X and Y are matrices then their dimensions must match. X > Y Compares each element of X against each element of Y and sets the corresponding element of the result to one if X is greater than Y, and zero otherwise. If both X and Y are matrices then their dimensions must match. X <= Y Compares each element of X against each element of Y and sets the corresponding element of the result to one if X is less than or equal to Y, and zero otherwise. If both X and Y are matrices then their dimensions must match. X >= Y Compares each element of X against each element of Y and sets the corresponding element of the result to one if X is greater than or equal to Y, and zero otherwise. If both X and Y are matrices then their dimensions must match. m : n m : k : n Returns a row vector starting with values m through n. If k is given then it is used as the increment between successive values. Otherwise, the increment is one. + X X + Y In the unary form, returns X. In the binary form, returns the sum of X and Y. If X and Y are both scalars then scalar addition is performed. If one is a scalar and the other is a matrix then the scalar value is added to each element of the matrix. If both are matrices then matrix addition is performed, and the dimensions of each must agree. - X X - Y In the unary form, returns the negative of X. In the binary form, returns the difference of X and Y. If X and Y are both scalars then subtraction is performed. If X is a matrix and Y is a scalar then Y is subtracted from each element of X. If X is a scalar and Y is a matrix then each element of X is subtracted from Y. If both are matrices then matrix subtraction is performed, and the dimensions of each must agree. X * Y Returns the product of X and Y. If X and Y are both scalars then scalar multiplication is performed. If one is a scalar and the other is a matrix then the matrix is scaled by the scalar value. If both are matrices then the matrix multiplication is performed, and the inner dimensions must agree. X \ Y Returns the "left division" of X and Y, or (1/X) * Y. If X and Y are matrices then an LU decomposition is used to compute the "inverse" of X. If X is a matrix but Y is a scalar then the true inverse of X is scaled by Y. X / Y Returns the "right division" of X and Y, or X * (1/Y). If X and Y are matrices then an LU decomposition (along with transposition) is used to compute the "inverse" of Y. If X is a scalar but Y is a matrix then the true inverse of Y is scaled by X. X % Y fmod (X, Y) Returns the modulo of X and Y. If X and Y are both scalars then the scalar remainder is computed. If X is a matrix and Y is a scalar then each element of X is computed modulo Y. If X is a scalar and Y is a matrix then X is computed modulo each element of Y. If both are matrices then each element of X is computed modulo each element of Y, and the dimensions of each must agree. m ^ n m ** n pow (m, n) Returns m raised to the power n, where m is non-negative or n is an integer value. Both m and n must be scalars. X ' Returns the transpose of X. The transpose of a scalar is itself. ! X not X Returns the logical negation of X. If X is a matrix then each element of X is negated. The logical negation of zero is one and the logical negation of a non-zero value is zero. ( X ) X ( ... ) In the first form, which may be used for enforcing precedence, the result is X. In the second form, if X is a matrix then the result is a subsection of the matrix (submatrix). The number of indices must be appropriate. If an index is a vector then it designates a series of rows or columns and must be contiguous. The special index : may be used to designate an entire row or column. If X is an array then the return value is the result of indexing the array. Otherwise, X is evaluated as a function and the remaining expressions are passed as arguments. The result is the return value of the function call. [ ... ; ... ; ... ] Returns a matrix. A semicolon (or return) separates one row for the next. Matrix elements on the same row are separated with commas. The matrix elements may be matrices or scalars, but all elements on the same row must have the same number of rows. Each row must also have the same number of columns. X . id Returns the field id of structure X. This operator is used to access members of the FElt data structures. any? (X) Returns true (one) if any element of X is non-zero. Otherwise, returns false (zero). X must be a matrix or a scalar. compact? (A) Returns true (one) if A is a compact-storage matrix. Otherwise, returns false (zero). every? (X) Returns true (one) if every element of X is non-zero. Otherwise, returns false (zero). X must be a matrix or a scalar. matrix? (A) Returns true (one) if A is a matrix (and not a scalar). Otherwise, returns false (zero). null? (A) Returns true (one) if A is null (has not been assigned a value). Otherwise, returns false (zero). scalar? (A) Returns true (one) if A is a scalar. Otherwise, returns false (zero). symmetric? (X) Returns true (one) if any X is a symmetric matrix or a scalar. Otherwise, false (zero). X must be a matrix or a scalar. V@EV5VBV3VDV FV FV FV?V@DV;V =V JV`AV:V1V6V8V5V1V4V7V9VHVHV`@VHW@DW3W@E W2 W2WWW@$W$#W`%+W /W&3W'7W;W (?WDWJWBOW UW(YW]W@cW@)fW*kW,pW@DtW-wW.|W0WWW@W0W0WJW@KWKW`LWLW`MWMWW@WWWW`W W` X X`! X!X@"X"X#%X.X:XHXYXjX tX X X X XX X XX X@Y Y 1YEY ]YWW+W7W?WDWJWOWYW]WpWWWWWWvY#W/W3W;WUWcWfWkWtWwW|WWWWWWWWWWWWWWWWWWXX XXXX~YYYYY Y%X.X:XHXYXjXtXXXXXXXXXXY!!=%&&'(())***+-./::=<<=<>===>>=[[]\]^andnotor||absceilcholcolscompactcosdeteigexpeyefabsfloorfmodhypotinvloglog10lunormonespowqrrandrowssinsqrttanzeroeszerosany?compact?every?matrix?null?scalar?symmetric?concatevalexithelphistoryincludeloadreadreadssavesystemtypewritewritesassembleclear_nodescompute_modescompute_stressesconstruct_forcesfind_dofsglobal_dofintegrate_hyperbolicintegrate_paraboliclocal_dofremove_constrainedrenumber_nodesrestore_numbersset_upsolve_displacementszero_constrainedoperatorsmathematical functionspredicate functionsmiscellaneous functionsfinite element functionscolumnsareafeltlengthvolumeadd_definitionremove_definition This file is part of the FElt finite element analysis package. Copyright (C) 1993-2000 Jason I. Gobat and Darren C. Atkinson This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. PAGERmorew Help is available on the following topics: %s: %*scopyright %s No help available for '%s'. \⍀PHC⍀P/*⍀P⍀P⍀Pߡ⍀Pˡơw⍀wP鲡譡b⍀bP陡蔡M⍀MP逡{8⍀8Pg]]]]^)^B^[^t^^$Ë$>3+W^]d]v`NlM`N,#c] WV^Y]@SX^Z ^ S] S] U] h`N bSS] )L] S S S `N `N v ] h^ YJ] A] 2* ] Z ,R(R RR RR RR QQ QQ QQ QQ QQ QQ QQy QQm QQk QQj QQf xQtQc lQhQ `Q\Q` TQPQ HQDQ +[#+ .=!6+7tQB 'AAXNJXl}dIQpj dn'xXrN_fabs_func_ceil_func_cos_func_exp_func_floor_func_fmod_func_hypot_func_log_func_log10_func_pow_func_sin_func_sqrt_func_tan_func_chol_func_cols_func_compact_func_det_func_eig_func_eye_func_inv_func_lu_func_norm_func_ones_func_qr_func_rand_func_rows_func_zeros_func_anyp_func_compactp_func_everyp_func_matrixp_func_nullp_func_scalarp_func_symmetricp_func_concat_func_eval_func_exit_func_help_func_history_func_include_func_load_func_read_func_reads_func_save_func_system_func_type_func_write_func_writes_func_area_func_felt_func_length_func_volume_func_add_definition_func_remove_definition_func_assemble_func_clear_nodes_func_compute_modes_func_compute_stresses_func_construct_forces_func_find_dofs_func_global_dof_func_integrate_hyperbolic_func_integrate_parabolic_func_local_dof_func_remove_constrained_func_renumber_nodes_func_restore_numbers_func_set_up_func_solve_displacements_func_zero_constrained_func___i686.get_pc_thunk.bx___i686.get_pc_thunk.axdyld_stub_binding_helper_dbl_array_sp___sF_RecycleData_TypeError_printf_fputs_strcmp_CoerceData_pclose_fprintf_popen_getenv_help_0_help_1_help_2_help_3_help_4_help_5_help_6_help_7_help_8_help_9_help_10_help_11_help_12_help_13_help_14_help_15_help_16_help_17_help_18_help_19_help_20_help_21_help_22_help_23_help_24_help_25_help_26_help_27_help_28_help_29_help_30_help_31_help_32_help_33_help_34_help_35_help_36_help_37_help_38_help_39_help_40_help_41_help_42_help_43_help_44_help_45_help_46_help_47_help_48_help_49_help_50_help_51_help_52_help_53_help_54_help_55_help_56_help_57_help_58_help_59_help_60_help_61_help_62_help_63_help_64_help_65_help_66_help_67_help_68_help_69_help_70_help_71_help_72_help_73_help_74_help_75_help_76_help_77_help_78_help_79_help_80_help_81_help_82_help_83_help_help_topics_functab_copyright_list_topics