{'fraction_non_alphanumeric': 0.022151898734177215, 'fraction_numerical': 0.002109704641350211, 'mean_word_length': 3.9427083333333335, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
THE BOUSSINESQ WEDGE AND THE Jk, L AND M INTEGRALS

This paper examines the application of the J k , L and M integrals, in complex-variable form, to the Boussinesq wedge. The wedge is symmetrical and subjected to a point couple and point forces at the apex of the wedge. In the case of a point couple acting at the wedge apex the J Y , L and M integrals are found to vanish for all wedge angles whereas J X displays a 1/r 3 path-dependence; where r is a radial dimension measured from the wedge apex. When the wedge is subjected to point forces at the wedge apex then J X and J Y are I/r path-dependent whereas L and M are path-independent. The property that the L and M integrals are path-independent for the Boussinesq wedge is applied to the problem of determining the modes I and II stress intensity factors for a corner-loaded edge crack in a half-plane subjected to both normal and parallel point forces to the free surface of the half-plane.